D.APPLE.ON&CO.,KewYork.  [ 


/r 


APPLETOUS'  MATHEMATICAL  &EEJES. 


f 


PEIMAEY    ARITHMETIC. 


BT 

G.  P.  QUACKENBOS,  LL.  D., 

AUTHOR  or 

"AN  ENGLISH  GRAMMAR;"  *' FIRST  LESSONS  IN  COMPOSITION  ;  "   "ADVANCED 
COURSE  OP  COMPOSITION  AND  RHETORIC;"    "A  NATURAL  PHILOSO- 
phy;" "illustrated  school  history  op  the  united 
states;"  "primary  history  op  the  united 
states ; "  etc. 


UPON     THE     BASIS     OP     THBW0EK8     OP 

GEO.  R.  PERKINS,  LL.D. 


KEW  YORK: 
D.  APPLETON  AND  COMPANY, 

1,  8,  AND  6  BOND  STEEET. 


'^~'''  '  "preface,  g^^' 

This  little  book,  the  first  of  our  Series  of  Arithmetics,  presup- 
poses no  knowledge  of  numbers  whatever.  It  tries  to  give  a  cor- 
rect idea  of  their  value,  both  absolute  and  relative,  by  treating 
them  concretely  as  well  as  abstractly  from  the  very  outset,  pictorial 
illustrations  being  freely  used  for  that  purpose.  We  have  not 
sought  in  its  pages  to  go  far,  but  to  go  thoroughly.  It  is  therefore 
confined  to  the  four  fundamental  operations,  a  very  brief  view  of 
fractions,  the  most  important  tables  of  moneys,  weights,  and  meas- 
ures, and  easy  exercises  under  them.  These  subjects,  it  is  believed, 
are  so  treated,  as  to  make  the  young  pupil  think  for  himself,  and  to 
lay  the  right  kind  of  foundation  for  a  mathematical  course.  One 
thing  is  taught  at  a  time,  and  great  care  has  been  taken  to  present 
every  thing  in  its  proper  place.  It  will  be  observed  that  through- 
out the  book  slate  exercises  go  hand  in  hand  with  mental  opera- 
tions. In  the  author^s  opinion,  they  are  indispensable,  from  the 
first,  for  inspiring  the  beginner  with  that  interest  in  the  subject 
which  is  essential  to  success. 

This  book  imposes  no  labor  on  the  teacher,  in  the  way  of  ex- 
plaining orally,  furnishing  examples,  &c.  It  is  thought  to  contain 
in  itself  all  that  is  needed.  The  author  would  only  ask  those  who 
use  it  to  be  sure  that  every  lesson  is  thoroughly  mastered,  before 
proceeding  to  the  next.  Each  principle  presented,  each  table, 
should  be  perfectly  understood  and  memorized  before  leaving  it, 
even  though  it  be  necessary  to  repeat  the  lesson  again  and  again. 
Time  saved  by  allowing  a  single  lesson  to  pass  unmastered,  will 
be  a  tenfold  loss  in  the  end. 

The  Roman  Notation  is  not  explained  in  this  volume ;  but  by 
means  of  the  numerals  used  in  the  lesson-headings  the  pupil  may 
readily  be  made  to  understand  it. 

Entered,  according  to  Act  of  Congress,  in  the  year  1868,  by 

D.  APPLETOJrA   CO., 

In  the  Clerk's  OflOice  of  the  District  Court  of  the  United  States  for  the 

Southern  District  of  New  York. 


auL. 


\ 


PRIMARY  ARITHMETIC. 


LESSON    I. 


Touch  your  head.  How  many  heads 
have  you  ?  One. 

Touch  your  eyes.  How  many  eyes 
have  you  ?      "  Two. 

Touch  the  joints  of  your  fore-finger. 
How  many  are  there  ?  Thkee. 

Touch  the  fingers  of  your  left  hand. 
How  many  are  there  ?    -^  Fouk. 

Touch  the  fingers  and  thumb  of  your 
left  hand.     How  many  do  they  make  ?       Five. 

When  we  say  one,  two,  tueee,  four,  five, 
what  do  we  do  ? 

Answer,  We  count. 

Count  five ;  count  four ;  count  three ;  count 
two. 

What  are  one,  two,  three,  four,  five,  called  ? 
Answer.  Numbers. 

Which  is  the  smallest  of  these  numbers  ? 
Which  is  the  greatest  of  these  numbers  ? 

54  I  \ 92 


A- 


;couNTmG. 


LSSSON    II. 

Count  the  birds  on 
this  branch.  How 
many  are  there  ?  Five. 

If  another  ah'ghts 
on  it,  how  many 
will  there  be  ?  Six, 

If  another  joins 
-them,  how  many 
will  that  make  ?      Seven. 
If  another 
comes,    how 
many  ?  Eight. 

^One  more 
will  make 
how  many?  Nine. 
And  one 
more,  how 
many  ?       Ten. 
Connt  six ;  count  seven  ;  eight ;  nine ;  ten. 
"Which  is  greater,  ten  or  five  ?     Two  or  six  ? 
What  do  we  use,  to  express  numbers  ? 
Answer.  Ten  characters,  called  Figures. 

Learn  the  names  of  these  ten  figures,  and  how 
to  make  them  neatly  on  your  slate. 

NAITGHT       ONB     TWO       THBKB      POUB       FIVE        BIX     BEVEN     EIGHT     NINB 


O       /    2 


-/    ^    d    7     ^  ^ 


COUNTING. — NUMERATION. — NOTATION. 


LESSON    III. 


Eleven 

// 

Twelve 

/2 

Thirteen 

/S 

Count  these  rabbits.     How  many  are  there  ? 
How  do  we  express  ten  with  figures  ? 
Answer.  By  putting  a  naught  after  a  one  (10). 
Learn  the  numbers,  going  up  from  ten : — 

Fourteen  / -4     Seventeen   /  y 
FifteeV      /S     Eighteen  '^^ 
Sixteen     /  d      Nineteen     /  p 
Twenty  ^     .     .     20 
Kead  these  numbers :  13 ;  7 ;  19  ;  11 ;  9  ;  2  ; 
20;  12;  5;  16;  3;  10;  4;  18;  6;  15;  8;  17. 
Write  in  figures,  six  ;  ten ;  three  ;  eighteen  ; 
eight ;  twenty ;  two  ;  twelve  ;  fourteen  ;  five. 

What  is  the  reading  of  numbers  called? 
Answer.  Nnmeration. 

What  is  the  writing  of  numbers  called? 
Answer.  "FTotation. 


COUNTING. 


LESSON    IV. 

Now  we  have  some  marks  in  diflPerent  rows. 
Count  those  in  each  row. 

The  number  of  marks  is  given  after  each  row ; 
then  come  the  written  figures  that  represent  this 
number,  then  the  printed  figures. 


I  I  I  I  I J 

mill 

iiiiiii  

iiiiiiii   

iiiiiiiii  

iiiiiiiiii  

iiiiiniiii  .  .  .  . 
iiiiiiiiiiii  .  .  .  . 
iiiiiiiiiiiii  .  .  . 
iiiiiiiiiiiiii   .  .  . 
iiiiiiiiiiiiiii  .  . 

Ml  I  II  I  I  I  I  I  I  I  I  I  I     .    . 


One 
Two 
Three 
Four 
,  Five 
Six 
Seven 
Eight 

!N'lNE 

Ten 

Eleven 

Twelve 

Thirteen 

Fourteen 

Fifteen 

Sixteen 

Seventeen 

Eighteen 

N'iNETEEN 

Twenty 


7 


// 
/^ 

/^ 
/^ 

^7 
y/ 

^0 


Which  is  greater,  twenty  or  ten  ? 


10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

11  or  18  ? 


COUNTING. 


LESSON  V. 

Learn  the  twenties  : — 

Twenty-one  21  I  Twenty-four  24 
Twenty-two  22  Twenty-five  25 
Twenty-three  23  |  Twenty-six      26 

In  the  twenties,  which  figure  remains  the 
same,  and  which  does  not  ? 

Answer,  The  left-hand  figure  remains  the 
same — 2.     The  right-hand  figure  changes. 

What  comes  after  29  ?    Answer,  Thirty  (30). 

Learn  the  thirties : — 


Twenty-seven  27 
Twenty-eight  28 
Twenty-nine    29 


Thirty-one       31 

Thirty-four 

34 

Thirty-seven    37 

Thirty-two       32 

Thirty-five 

35 

Thirty-eight    38 

Thirty-three    33 

Thirty-six 

36 

Thirty-nine      89 

What  is  the  left-hand  figure  in  all  the  thirties  ? 
Which  figure  changes  ? 

What  comes  after  39  ?      Answer,  Forty  (40). 
Learn  the  forties  : — 


Forty-one 

41 

Forty-four 

44 

Forty-seven     47 

Forty-two 

42 

Forty-five 

45 

Forty-eight     48 

Forty-three 

43 

Forty-six 

46 

Forty-nine       49 

Fifty  ....     50 

Which  is  greater,  fifty  or  forty?  49  or  39? 
28  or  38?    26  or  17?    9  or  15  ?    15  or  30? 

Count  from  1  to  60.  Count  from  20  to  1 
backwards ;  twenty^  nineteen^  eighteen^  &c. 


8 

OOUiniNG. 

LESSON    VI. 

Learn  the  numbers,  going  up  from  fifty : — 

Fifty 

60 

Sixty-seven      67 

Eighty-four      84 

Fifty-one 

51 

Sixty-eight       68 

Eighty-five       85 

Fifty-two 

52 

Sixty-nine        69 

Eighty-six        86 

Fifty-three 

53 

Seventy            70 

Eighty-seven    87 

Fifty-four 

54 

Seventy-one      71 

Eighty-eight     88 

Fifty-five 

55 

Seventy-two     72 

Eighty-nine      89 

Fifty-six 

56 

Seventy-three  73 

Ninety              90 

Fifty-seven 

57 

Seventy-four     74 

Ninety-one       91 

Fifty-eight 

58 

Seventy-five     75 

Ninety-two       92 

Fifty-nine 

59 

Seventy-six      76 

Ninety-three     93 

Sixty 

60 

Seventy-seven  77 

Ninety-four      94 

Sixty-one 

61 

Seventy-eight  78 

Ninety-five       95 

Sixty-two 

62 

Seventy-nine    79 

Ninety-six        96 

Sixty-three 

63 

Eighty              80 

Ninety-seven    97 

Sixty-four 

64 

Eighty-one       81 

Ninety-eight    98 

Sixty-five 

65 

Eighty-two       82 

Ninety-nine      99 

Sixty-six 

66 

Eighty-three    83 

One  hundred  100 

How  many  figures  does  100  contain  ? 

What  is 

the  greatest  number  that  can  be  ex- 

pressed  with  two  figures  ?                   Answer,  99. 

What  is 

the  greatest  number  that  can  be  ex- 

pressed  with  one  figure  ?                       Ansvjer.  9. 

Name  in  order  the  numbers  between  1  and 

100  that  contain  naught. 

Ans.  10 

,  20,  30,  40,  50,  60,  70,  80,  90,  100. 

COUNTING. 


LESSON   VII. 


Here  is  a  factory  ten  stories  high.  How  many 
windows  are  there  in  each  story  ? 

Count  the  windows  in  the  two  lowest  stories. 
How  many  do  you  find?  How  many  rows  of 
10  each  make  20  ?     How  many  tens  in  20  ? 

Count  the  windows  in  the  three  lowest  stories. 
How  many  tens  in  thirty  ? 

Add  another  row  of  windows,  and  how  many 
do  you  find  ?     How  many  tens  in  forty  ? 

Count  the  windows  in  the  five  lowest  rows. 
How  many  tens  in  fifty  ? 

How  many  tens  in  60  ?  How  many  tens  in 
70  ?  How  many  tens  in  eighty  ?  How  many 
tens  in  90  ? 

Count  all  the  windows.  How  many  are  there  ? 
How  many  rows  of  10  each  make  100  ?  How 
many  tens  in  one  hundred  ? 


10  UNITS. TENS. 


LESSON   VIII. 

Learn  this  table  : — 


20  is  2  tens. 
30  is  3  tens. 
40  is  4  tens. 
50  is  5  tens. 


60  is  6  tens. 
70  is  7  tens. 
80  is  8  tens. 
90  is  9  tens. 


Which  figure  shows  the  number  of  tens  ? 
Answer.  The  second,  or  left-hand  figure. 

What  is  the  second  place  called  ? 
Answer,  The  place  of  tens. 

What  is  the  first,  or  right-hand  place  called  ? 
Answer.  The  place  of  units. 

Write  down  22.     What  figures  do  you  use  ? 

Have  these  twos  the  same  value  ? 
Answer.  No.     The  2  in  the  second  place  is 
ten  times  as  great  as  the  2  in  the  first  place. 

Why  is  this  ? 

Answer.  Because  the  2  in  the  second  place 
denotes  two  tens^  or  twenty ;  the  2  in  the  first 
place  denotes  two  units^  or  two. 

What,  then,  is  the  effect  of  removing  a  figure 
from  the  first  place  to  the  second  ? 

Answer.  Its  value  is  increased  ten  times ;  20 
is  ten  times  as  great  as  2. 

Write  down  the  numbers  from  1  to  100. 


UNITS. TENS.  11 


LESSON    IX. 

How  do  you  write  six  tens  ? 

Ans,  6  in  the  second  place  denotes  six  tens. 
As  there  are  no  units,  I  put  a  0  after  it — 60. 

How  do  you  write  six  tens,  one  unit  ? 

Arts.  6  in  the  second  place  denotes  six  tens  ; 
1  in  the  first  place  denotes  one  unit — 61. 

Read  this  number.  Arts,  Sixty-one. 

How  must  a  column  of  numbers  be  written  ? 
Ans.  So  that  units  may  stand  under  units,  and 
tens  under  tens. 

Write  the  following : — Four  tens,  three  units ; 
nme  tens,  nine  units ;  three  tens,  seven  units ; 
eight  tens,  two  units ;  five  tens,  two  units ;  two 
tens,  five  units ;  one  ten  ;  seven  tens. 

Kead  the  numbers  just  written. 

Mention  the  tens  and  units  in  the  following 
numbers,  and  then  read  them : — 80  {eight  tens^ 
eighty) ;  75  {seven  tens^  five  units^  seventy-five) ; 
69;  93;  41;  28;  7;  50;  17;  32;  84;  22;  61; 
14  ;  57  ;  46  ;  70  ;  11 ;  98 ;  23. 

Which  is  greater,  a  ten  or  a  unit  ? 

How  can  you  turn  three  into  thirty  ? 

Count  from  100  to  75  backwards.  Count 
from  50  to  20  backwards. 

Write  down  in  columns  the  numbers  in  order, 
going  backwards  from  100  to  1. 


12  HUNDREDS. 


LESSON    X. 

How  much  do  10  tens  make  ? 

Ans.  One  hundred — 100. 

Which  figure  shows  the  number  of  hundreds  ? 

Ans.  The  third  figure — 1. 

How,  then,  do  we  write  two  hundred  ? 

Ans.  By  putting  a  2  in  the  third  place — 200. 

Learn  the  hundreds : — 


One  hundred  100 

Two  hundred  200 

Three  hundred  300 

Four  hundred  400 


Five  hundred  500 

Six  hundred  600 

Seven  hundred  TOO 

Eight  hundred  800 
Nine  hundred  .     .     .     900 

How  many  times  greater  is  1  in  the  third 
place  than  1  in  the  second  place  ? 

Ans,  Ten  times  ;  100  is  ten  times  10. 

What  is  the  effect,  then,  of  removing  a  figure 
one  place  to  the  left  ? 

Arts,  Its  value  is  increased  ten  times. 

Name  the  places,  going  from  right  to  left. 

Atis.  Units,  tens,  hundreds. 

Count  from  100  to  200.  Thus  \—One  lirni- 
dred  cmd  one^  one  hundred  and  two^  &c. 

Write  the  numbers  from  100  to  200.     Thus : 

101  104    107    110     113     116 

102  105     108     111     114    117 

103  106     109     112     115     118,  &c. 


NUMERATION. NOTATION.  13  J 

LESSON    XI. 

What  is  Numeration  ? 

Answer.  The  art  of  reading  numbers. 

What  is  Notation  ? 

Answer,  The  art  of  writing  numbers. 

EXERCISE    IN    NUMERATION. 

Read  the  following  numbers  : — 


198 

912 

15 

853 

4 

909 

611 

1 

268 

309 

200 

88 

82 

79 

41 

470 

224 

625 

Y03 

816 

526 

6 

36 

64 

434 

349 

62 

518 

147 

517 

EXERCISE   IN   NOTATION. 

Write  these  numbers  in  figures  : — 
Eighty-three ;   Fourteen ;   Two  hundred  and 
sixty  ;  Nine  hundred  and  forty-eight ;  One  hun- 
dred and  nine ;    Twelve  ;    Ninety-one ;     Seven 
hundred  and  fifty-seven ;  Thirty-four. 

Three  hundred  and  fifteen  ;  Seventy-two  ; 
Six  hundred  and  twenty-four  ;  One  hundred  ; 
Four  hundred  and  seven  ;  Eight  hundred  and 
eleven ;  Eighty-eight ;  Five  hundred  and  forty ; 
Fifty  ;  Seven  hundred  and  twenty  ;  Ninety-nine. 

Counting.— Count  from  800  to  900. 


14 


ADDITION. 


LESSON    XII. 


Look  at  the  picture.  You  see  one  diimney  in 
one  part  of  the  roof,  and  one  chimney  in  another 
part;  how  many  chimneys  do  you  see  in  all? 
Count  them.     One  and  one  are — how  many  ?. 

One  sheep  is  feeding  by  itself,  and  two  sheep 
are  feeding  together ;  how  many  sheep  are  there 
in  all  ?     One  and  two  are  — . 

One  boy  and  three  girls  are  walking.  How 
many  in  all  are  walking  ?     One  and  three  are  — . 

One  dog  is  lying  down,  four  dogs  are  running ; 
how  many  dogs  are  there  altogether  ?  One  and 
four  are  — . 


ADDITION.  15 


There  is  one  window  on  one  side  of  the  house, 
and  five  windows  on  another.  How  many  win- 
dows are  there  altogether  ?     One  and  five  are  — . 

There  is  one  girl  jumping  the  rope,  and  six 
girls  not  jumping  it.  How  many  girls  are  there 
in  all  ?     One  and  six  are  — . 

On  the  lawn  we  see  one  boy  and  seven  girls ; 
counting  the  boy  and  girls  together,  how  many 
are  on  the  lawn?     One  and  seven  are  — . 

One  tree  stands  on  one  side  of  the  house,  and 
eight  trees  on  the  other.  How  many  trees  do 
you  count  altogether  ?     One  and  eight  are  — . 

One  chicken  by  itself,  and  nine  chickens  in  a 
group  ;  how  many  chickens  in  all  ?  One  and 
nine  are  — . 

One  hen  and  ten  chickens  ;  counting  hen  and 
chickens  together,  how  many  do  you  find  ?  One 
and  ten  are  — . 

What  you  have  just  answered,  will  now  be 
put  in  a  table.     Learn  it  perfectly. 


1  and  1  are  2. 

1  and     6  are 

7. 

1  and  2  are  3. 

1  and    7  are 

8. 

1  and  3  are  4. 

1  and     8  are 

9. 

1  and  4  are  5. 

1  and    9  are 

10. 

1  and  5  are  6. 

1  and  10  are 

11. 

When  you  put  numbers  together,  to  find  ho^;^ 
much  they  make,  what  is  the  process  called  ? 
A71S,  Addition. 


16 


ADDITION. 


LESSON    ZIII. 

What  is  Addition? 

Ans.  Addition  is  the  process  of  uniting  two 
or  more  numbers  in  one. 

When  you  unite  two  or  more  numbers  in  one, 
what  do  you  find?  Ans,  I  find  their  Sum. 


Two  men  are  riding ;  one  is  walking  by  their 
side ;  how  many  men  in  all  ?    Add  2  and  1. 

Jane  has  two  kittens  ;  her  sister  also  has  two. 
How  many  kittens  have  both  ?     Add  2  and  2. 

Jane  had  two  dollars,  and  her  father  gave  her 
three  more.     How  many  had  she  then  ? 


Learn  the  Tables  so  as  to  say  them  forward 
and  backward,  in  order  or  skipping  about. 


2  and  1  are  3. 
2  and  2  are  4. 
2  and  3  are  5. 
2  and  4  are  6. 

2  and  5  are  7. 


2  and  6  are  8. 
2  and  7  are  9. 
2  and  8  are  10. 
2  and  9  are  11. 
2  and  10  are  12. 


ADDITION.  17 


LESSON    XIV. 


3  and  1  are  4. 

3  and  2  are  5. 

3  and  3  are  6. 

3  and  4  are  7. 

3  and  5  are  8. 


3  and  6  are  9. 
3  and  7  are  10. 
3  and  8  are  11. 
3  and  9  are  12. 
3  and  10  are  13. 


[Let  the  pupil  in  all  cases  add  each  number  as  a  whole, 
and  not  by  counting  or  taking  one  unit  at  a  time.  Say  three 
and  three  are  six;  not  three,  four,  Jive,  six.] 


1.  A  regiment  inarched  three  miles  before 
dinner,  and  five  miles  after  dinner.  How  far 
did  it  march  in  all  ?    Add  3  and  5. 

2.  If  you  have  3  marbles  in  one  pocket,  and 
7  in  another,  how  many  have  you  in  both  ? 

3.  Three  horses  are  in  the  stable,  and  six  are 
in  the  field.     How  many  horses  in  all  ? 

4.  Euth  bought  three  books;  she  had  ten 
books  before.     How  many  has  she  now  ? 

Now  you  have  a  few  examples  in  addition  for 
your  slate.  Copy  the  figures  in  each  column, 
add  them,  and  write  the  sum  below  the  line. 

1127859      10 
12331321 


1 

10 

9 

8 

74 

65 

7 

1 

1 

1 

2 

10 

21 

1 

1 

1 

2 

1 

12 

11 

2 

18 


ADDITION. 


LESSON    XV. 


"1^  /\  /\  /\ 


J/   >/  \/   \/ 


How  many  are  1  and  4  ? 

How  many  are  4  and  1  ? 

How  many  are  2  and  4  ?    4  and  2  ? 

How  many  are  3  and  4  ?     4  and  3  ? 

When  you  are  adding  numbers,  does  it  make 
any  difference  whicli  you  take  first  ? 

Here  are  four  eggs  in 
one  bird's -nest,  four  in 
another ;  count  how  many 
there  are  in  both.  Add 
4  and  4. 


Four  kittens  are  running  one  way,  and  five 
the  other ;  how  many  in  all  ?     4  and  5  make  — „ 


Four  rats  and  six  rats  make  how  many  rats  ? 
How  many  are  4  and  6  ? 


4  and  1  are  5. 

4  and     6  are  10. 

4  and  2  are  6. 

4  and     Y  are  11. 

4  and  3  are  7. 

4  and     8  are  12. 

4  and  4  are  8. 

4  and     9  are  13. 

4  and  5  are  9. 

4  and  10  are  14. 

QUESTIOJ^S   IN   ADDITIOK.  19 

liSSSON    XVI. 

1.  Harry  gets  four  good  marks  on  Monday,  / 
and  seven  on  Tuesday ;  how  many  does  lie  get 
both  days  ?     How  many  do  4  and  7  make  ? 

2.  I  have  four  fingers  on  each  hand ;  how 
many  have  I  on  both  ?  What  is  the  sum  of  4 
and  4? 

3.  If  four  cars  leave  in  one  train,  and  ten  in 
another,  how  many  leave  in  both  ?    Add  4  and  10. 

4.  Ida  had  one  pencil,  then  she  bought  three, 
and  the  next  day  her  father  gave  her  seven  more ; 
how  many  had  she  then  in  all?  1,  3,  and  7, 
make  how  many  ? 

5.  A  toyman  sold  two  dolls  in  the  morning, 
two  in  the  afternoon,  and  nine  in  the  evening ; 
how  many  did  he  sell  altogether  ?  2  and  2  added 
to  9  make  how  many  ? 

6.  If  I  give  four  dollars  for  a  vest,  and  eight 
dollars  for  a  coat,  how  much  do  both  cost  me  ? 

Add  the  following  numbers  on  your  slate.  Be 
sure  to  set  units  under  units,  tens  under  tens. 

Add  twenty-three  and  thirty-four.  Add  one 
hundred,  twelve,  and  three  hundred  and  forty- 
three.  Add  forty-four  to  four  hundred  and  one. 
Add  four  and  eleven.  Add  seventy-four  and 
two  hundred  and  two.  Add  ninety-four  and 
three  hundred. 


20 


ADDITION. 


LESSON  XVII. 

How  many  are  one  and  five  ?  ->$•  ">HHHHc 
How  many  are  five  and  one  ?   •>r-/Hc">Hr  '/<- 
How  many  are  2  and  5  ?     5  and  2  ? 
How  many  are  3  and  5  ?     5  and  3  ? 


Five  lilies  and  four  lilies  are  how  many  lilies? 


Five  boys  are  sailing  in  one  boat,  and  five  in 
another.     Count  how  many  there  are  in  both. 


Five  tops  are  lying  on  the  floor,  and  six  are 
spinning ;  how  many  do  you  see  in  all  ? 

How  many  are  5  and  7?       Mill    Illllll 
How  many  are  5  and  8?       |||||    II  Mill  I 
How  many  are  5  and  9?       Mill    I  Mill  I  II 
How  many  are  5  and  10?     Mill    I  Mill  MM 
Which  is  the  greater,  five  or  ten  ? 


5  and  1  are    6. 

5  and     6  are  11. 

5  and  2  are     7, 

5  and     7  are  12. 

5  and  3  are     8. 

5  and     8  are  13. 

5  and  4  are    9. 

5  and     9  are  14. 

5  and  5  are  10. 

5  and  10  are  15. 

QUESTIONS   IN    ADDITION.  21 

LESSON    XVIII. 

1.  Five  years  ago  Mary  was  nine  years  old ; 
how  old  is  she  now  ?     How  much  are  5  and  9  ? 

2.  We  have  five  toes  on  each  foot ;  how  many 
toes  have  we  in  all  ?     What  is  the  sum  of  5  and  5  ? 

3.  Horace  has  five  marbles  in  one  bag,  and 
ten  in  another  ;  how  many  has  he  in  both  ?  Add 
5  and  10. 

4.  Five  pigs  are  in  the  orchard,  and  seven  in 
the  sty.     How  many  pigs  are  there  altogether  ? 

6.  Louise  has  three  cents,  Mary  two,  and 
George  eight ;  how  many  cents  have  all  three  ? 

6.  Susan  has  four  books  ;  if  her  brother  gives 
her  one  more,  and  her  sister  two,  how  many  books 
will  she  have?    Add  4,  1,  and  2. 

7.  Eichard  caught  five  fish,  and  Ben  six  ;  how 
many  did  both  catch  ?     How  many  are  5  and  6  ? 

8.  The  first  story  of  a  house  contains  two 
rooms,  the  second  three,  and  the  third  three  ;  how 
many  rooms  does  the  whole  house  contain? 

Here  are  some  examples  for  your  slate.  Eead 
each  of  the  numbers  added,  and  also  the  answers. 


(10) 

(11) 

(12) 

(13) 

(14) 

(15) 

4: 

403 

927 

8 

5 

765 

14 

515 

20 

610 

372 

121 

51 

30 

32 

41 

112 

102 

' 

22 


ADDITION. 


LESSON    XIZ 


\/  \/  \f  \f^\^^, 

7  r*/  C/  \"i  **/  r' 


How  many  are  one  and  six  ? 

How  many  are  six  and  one  ?    ->r*>Hr"-/Hwr  '/c 

How  many  are  2  and  6  ?     6  and  2  ? 

How  many  are  3  and  6  ?     6  and  3  ? 

How  many  are  4  and  6  ?     6  and  4  ? 

How  many  are  5  and  6  ?     6  and  5  ? 

Six  flies  and  six  flies  are  how  many  flies  ? 


Six  sqnirrels  are  eating,  seven  are  running; 
connt  how  many  there  are  in  all. 


If  you  put  six  forks  and  eight  forks  together, 
how  many  will  yon  have  ? 

How  many  are  6  and  9?       |||||!    MINMII 
How  many  are  6  and  10?     |1||||    111  Hi  HI  | 


6  and  1  are    7. 

6  and     6  are  12. 

6  and  2  are     8. 

6  and    7  are  13. 

6  and  3  are    9. 

6  and     8  are  14. 

6  and  4  are  10. 

6  and     9  are  15. 

6  and  5  are  11. 

6  and  10  are  16. 

QUESTIONS   IN   ADDITION,  23 

IiESSON    XX. 

1.  Troy  is  six  miles  above  Albany,  and  Lan- 
singburg  is  three  miles  farther ;  how  far  is  Lan- 
singburg  from  Albany  ?   6  and  3  make  how  many  ? 

2.  If  I  have  6  dollars  in  my  pocket,  and  9  in  my 
purse,  how  mnch  have  I  in  all  ?    Add  6  and  9. 

3.  Three  dogs,  and  three  dogs,  and  three  dogs, 
make  how  many  ?    How  many  are  3,  3,  and  3  ? 

4.  Two  ships,  four  schooners,  and  ten  brigs, 
are  in  port ;  how  many  vessels  does  that  make  in 
all  ?    What  is  the  sum  of  2,  4,  and  10  ? 

5.  A  baker  sold  six  loaves  of  wheat  bread,  and 
two  of  rye  ;  how  many  loaves  did  he  sell  in  all  ? 

6.  Mary  gave  a  poor  man  six  cents,  and  Kate 
gave  him  five ;  how  much  did  he  receive  from 
both  ?     How  much  are  6  and  5  ? 

7.  If  six  horses  are  in  the  stable,  and  I  put  in 
eight  more,  how  many  will  be  there  then  ? 

8.  Six  goats  and  one  goat  make  how  many  ? 

9.  Six  shoes  in  one  drawer,  and  six  in  another, 
make  how  many  in  all  ? 

Add  the  following  numbers  on  your  slate : — 


(10) 

(") 

(12) 

(13) 

(14) 

(IS) 

80 

92 

43 

66 

730 

80 

31 

25 

653 

42 

10 

605 

26 

41 

203 

11 

256 

113 

137 

798 

24 


.UDDmON". 


^/  \f  \f  \f  \f  \/  \f 

*/ c*/ v**/ r*/ c"/ r^  x"*/ \* 


LBSSON    XXI. 

How  many  are  1  and  7  ? 

How  many  are  7  and  is      /  x*  /  r*  -">  v-*  r*/  r*/  ;•    ">  x- 

How  many  are  2  and  7  ?     7  and  2  ? 

How  many  are  3  and  7  ?     7  and  3  ? 

How  many  are  4  and  7  ?     7  and  4  ? 

How  many  are  5  and  7  ?     7  and  5  ? 

How  many  are  6  and  7  ?     7  and  6  ? 

Mary  has  a  bunch  of   seven 

cherries,  and  buys  seven  more ; 

how  many  has  she  then  i   Count 

and  see. 


Seven  boys  and  eight  girls  make  how  many 
children  in  all  ?     How  many  are  7  and  8  ? 

^  W  W  W  ^  W  W  Seven  wine  glasses  in  one 

%I%l%I\i%l%i  _  ^<^^  ^d  iiiiie  in  another 
make   how  many   in   all  ? 
How  many  are  7  and  9  ? 
How  many  are  7  and  10  ? 


7  and  1  are     8. 

7  and     6  are  13. 

7  and  2  are     9. 

7  and     7  are  14. 

7  and  3  are  10. 

7  and     8  are  15. 

7  and  4  are  11. 

7  and     9  are  16. 

7  and  5  are  12. 

7  and  10  are  17. 

QUESTIONS   IN   ADDITION.  25 


LESSON   XXII. 

1.  To  get  home,  I  shall  have  to  go  seven  miles 
by  steamboat,  and  five  by  stage ;  how  far  will  1 
have  to  travel  ?     What  is  the  sum  of  7  and  5  ? 

2.  A  farmer  had  seven  rooms  in  his  house,  and 
built  a  wing  with  three  rooms  more ;  how  many 
rooms  had  he  then  ?     How  many  are  7  and  3  ? 

3.  A  gardener  set  out  three  lilacs,  four  roses, 
and  ten  verbenas ;  how  many  plants  did  he  set 
out  in  all?    Add  3,  4,  and  10. 

4.  Mary  dressed  five  dolls  for  the  fair,  Augusta 
two,  and  Helen  seven ;  how  many  did  all  three 
dress  ?     How  many  are  5,  2,  and  7  ? 

6.  If  my  black  hen  has  seven  chickens,  and 
my  white  hen  nine,  how  many  have  both  ? 

6.  How  far  will  a  horse  go  in  2  hours,  if  he 
travels  7  miles  the  first  hour,  and  6  the  second  ? 

7.  How  many  are  6  and  4  ?  6  and  9  ?  4  and 
7?  7and4?  7and2?  3andl0?  2and8? 
1,  6,  and  1  ?  4,  3,  and  8  ?  6,  1,  and  6  ?  1  and 
7?    6  and  3? 

Here  are  some  examples  for  your  slate.  Make 
your  figures  neatly.  Kead  each  number,  and  tell 
whether  the  upper  or  lower  one  is  the  greater. 

(8)  (9)  (10)  (11)  (12)  (13) 

163    329    48    856    775    507 
425    670    731    132    11    182 


26 


ADDITION. 


IiESSON    XXIII. 

How  many  are  1  and  8  ?    •>(*  "vc-JC—X—X—X- 
How  many  are  8  and  1  ?    "/  (— >  H  c"/  c"/  r*/ 

How  many  are  2  and  8  ? 
How  many  are  3  and  8  ? 
How  many  are  4  and  8  ? 
How  many  are  5  and  8  ? 
How  many  are  6  and  8  ? 
How  many  are  7  and  8  2 


c'/r'/C'/C/C 

8  and  2? 
8  and  3  ? 
8  and  4? 
8  and  5? 
8  and  6? 
8  and  73 


Eight  doves  in  one  group,  and  eight  in  another, 
make  how  many  in  all  ?     How  many  are  8  and  8  ? 
Eight  rounds  in  one  ladder,  and 
nine  rounds  in  another,  make  how 
many  rounds  in  all  ?    What  is  the 
sum  of  8  and  9  ? 

Eight  spokes  are  in  one 
wheel,  and  ten  in  another ;  how 
many  are  in  both?  8  and  10 
are  — . 


8  and  1  are     9. 

8  and     6  are  14.          ^ 

8  and  2  are  10. 

8  and    7  are  15. 

8  and  3  are  11. 

8  and     8  are  16.  ,         , 

8  and  4  are  12. 

8  and     9  are  17. 

8  and  5  are  13. 

8  and  10  are  18. 

QUESTIONS  IN   ADDITION,  27 

LESSON   XZIV. 

1.  A  lady  bought  eight  cents'  worth  of  needles, 
and  six  cents'  worth  of  thread  ;  how  much  did  she 
lay  out  ?     How  many  are  8  and  6  ? 

2.  Eight  birds  are  sitting  on  a  bush ;  if  ten 
more  alight  by  their  side,  how  many  will  there 
be  ?    What  is  the  sum  of  8  and  10  ? 

3.  If  I  spend  six  dollars  for  clothes,  two  dol- 
lars for  books,  and  three  dollars  for  groceries,  how 
much  do  I  spend  in  all  ?     6,  2,  and  3,  are  — . 

4.  Sarah  has  three  rabbits,  Kuth  five,  and 
Herman  seven.  If  Sarah  and  Euth  give  theirs 
to  Herman,  how  many  will  he  have  ?  Add  3, 
5,  and  7. 

5.  If  a  dairy-maid  makes  eight  pounds  of 
butter  one  day,  and  four  the  next,  how  many 
does  she  make  in  all  ?     How  many  are  8  and  4  ? 

6.  How  many  boys  will  two  benches  hold, 
if  one  holds  eight  and  the  other  nine?  Add 
8  and  9. 

7.  Add  on  your  slate  seventeen  and  eighty. 

8.  Add  twenty  to  two  hundred  and  twelve. 

Kead  these  numbers ;  add  them. 


(9) 

(10) 

(11) 

(12) 

(13) 

(U) 

(15) 

63 

57 

91 

40 

21 

35 

Y2 

82 

81 

88 

88 

-  85 

84 

85 

145 

157 

28 


ADDITION. 


LSSSON    XXV. 

How  many  are  one  and  nine  ?     f  ttftftttt 

How  many  are  nine  and  one  ?     ttttttttt  t 

How  many  are  2  and  9  ?     9  and  2  ? 

How  many  are  3  and  9  ?     9  and  3  ? 

How  many  are  4  and  9  ?     9  and  4  ? 

How  many  are  5  and  9  ?     9  and  5  ? 

How  many  are  6  and  9  ?     9  and  6  ? 

How  many  are  7  and  9  ?     9  and  7  ? 

How  many  are  8  and  9  ?     9  and  8  ? 

4-  ^  Nine   stars    in    one 

other,  make  how  many 
Count  and  see. 


stars  in  all  ? 


If  there  are  nine  cannon- 
balls  in  one  pile,  and  ten  in 
another,  how  many  balls  are 
there  in  both  ?    What  is  the  sum  of  9  and  10  J 

A  jeweller  has  nine  watches  in  his  safe,  and 
five  on  his  counter  ;  how  many  has  he  in  all  ? 


9  and  1  are  10. 

9  and     6  are  15. 

9  and  2  are  11. 

9  and    7  are  16. 

9  and  3  are  12. 

9  and     8  are  17. 

9  and  4  are  13. 

9  and    9  are  18. 

9  and  5  are  14. 

9  and  10  are  19. 

QUESTIONS   IN   ADDITION.  29 

LESSON    XXVI. 

1.  If  Harry  has  nine  dollars  in  the  bank,  and 
four  in  his  pocket,  how  much  has  he  in  all  ? 

2.  A  milkman  sold  one  customer  three  quarts 
of  milk,  another  six  quarts,  and  a  third  seven ; 
how  many  quarts  did  he  sell  all  three?  What  is 
the  sum  of  3,  6,  and  7  ? 

3.  Blanche  has  two  canary  birds,  Eose  seven, 
and  Alice  three ;  if  Eose  and  Alice  give  theirs 
to  Blanche,  how  many  will  she  then  have  ? 

4.  If  one  field  yields  nine  bushels  of  potatoes, 
and  another  ten,  how  much  do  both  yield  ? 

5.  If  Frank  gets  nine  good  marks  in  the  morn- 
ing, and  five  in  the  afternoon,  how  many  does  he 
get  during  the  day  ?     How  many  are  9  and  5  ? 

6.  Nine  currants  on  one  string,  and  nine  on 
another,  make  how  many  currants  in  all  ?  9  and 
9  are  how  many  ? 

7.  There  are  nine  eggs  in  one  hen's  nest,  and 
six  in  another ;  if  we  put  the  eggs  together,  how 
many  will  there  be  ?   What  is  the  sum  of  9  and  6  ? 

8.  What  is  the  sum  of  1,  8,  and  2  ? 

Eead  the  following  numbers.    Add  them. 

(9)  (10)  (11)  (12)  (13)  (14) 

510    601    17    82    140    91 

67    95    700    33    806    45 

412    203    41    62    42    52 


30  ADDITION. 


IiBSSON   ZXVII. 


10         1 
1       10 


How  many  are  one  and  ten  ? 

How  many  are  ten  and  one  ? 

How  many  are  2  and  10  ?     10  and  2  ? 

How  many  are  3  and  10  ?     10  and  3  ? 

How  many  are  4  and  10  ?     10  and  4  ? 

How  many  are  5  and  10  ?     10  and  5  ? 

How  many  are  6  and  10  ?     10  and  6  ? 

How  many  are  7  and  10  ?     10  and  7  ? 

How  many  are  8  and  10  ?    10  and  8  ? 

How  many  are  9  and  10  ?     10  and  9  ? 

How  many  are  two  tens  ?    Ans.  Twenty.    10 

How  many  are  ten  and  ten  ?  15 

You  have  eight  fingers  and  two  thumbs  ;  I 
have  the  same.  How  many  fingers  and  thumbs 
have  we  together?  What  is  the  sum  of  8,  2, 
and  10? 

A  dime  is  worth  ten  cents;  a  half-dime  is 
worth  five  cents.  How  many  cents  are  both 
together  worth  ?    How  many  are  10  and  5  ? 

What  is  the  sum  of  7,  3,  and  8  ? 

What  is  the  sum  of  6,  4,  and  3  ? 


10  and  1  are  11. 

10  and  2  are  12. 

10  and  3  are  13. 

10  and  4  are  14. 

10  and  5  are  15. 


10  and  6  are  16 

10  and  7  are  17. 

10  and  8  are  18. 

10  and  9  are  19 

10  and  10  are  20. 


THOUSANDS. 


31 


LESSON  ZXVIII. 

What  is  the  greatest  number  that  can  be 
expressed  with  one  figure? 

Ans.  Nine  (9). 

If  you  add  1  to  9,  what  do  you  get  ? 

Ans.  Ten  (10). 

What  is  the  greatest  number  that  can  be 
expressed  with  two  figures  ? 

Ans.  Ninety-nine  (99). 

If  you  add  1  to  99,  what  do  you  get  ? 

Ans.  One  hundred  (100). 

What  is  the  greatest  number  that  can  be 
expressed  with  three  figures  ? 

Ans.  Nine  hundred  and  ninety-nine  (999). 

If  you  add  1  to  999,  what  do  you  get  ? 

Ans.  One  thousand  (1000). 

How  many  figures  are  used  in  writing  1000  ? 

What  figure  shows  the  number  of  thousands  ? 

Ans.  The  fourth  figure — 1. 

How,  then,  do  we  write  two  thousand? 

Ans.  By  putting  a  2  in  the  fourth  place. 

Learn  the  thousands : — 


One  thousand  1000 
Two  thousand  2000 
Three  thousand  3000 
Four  thousand  4000 
Nine  thousanc . 


Five  thousand  5000 

Six  thousand  6000 

Seven  thousand  7000 

Eight  thousand  800.0 
.     .     .  9000 


32  EXERCISE  IN  NOTATION. 

LESSON   XXIX. 

Learn  the  even  hundreds  between  1000  and 
2000  :— 
1100,  one  thousand  one  hundred,  or  eleven  hundred. 
1200,  one  thousand  two  hundred,  or  twelve  hundred, 
1300,  one  thousand  three  hundred,  or  thirteen  hundred. 
1400,  one  thousand  four  hundred,  or  fourteen  hundred. 
1500,  one  thousand  five  hundred,  or  fifteen  hundred. 
1600,  one  thousand  six  hundred,  or  sixteen  hundred. 
IVOO,  one  thousand  seven  hundred,  or  seventeen  hundred. 
1800,  one  thousand  eight  hundred,  or  eighteen  hundred. 
1900,  one  thousand  nine  hundred,  or  nineteen  hundred. 
2000,  two  thousand. 

Write  on  your  slate  the  numbers  between  1000 
and  1100,  and  then  read  them.     Thus  : 

1001,  one  thousand  and  one. 

1002,  one  thousand  and  two,  &c 
"Write  one  thousand  and  ten.  1010. 
Write  two  thousand  and  ten.                    2010. 
Write  1  thousand  2  hundred  and  ten.      1210. 
Write  8  thousand  2  hundred  and  ten.      8210. 
Write  one  thousand  four  hundred.           1400. 
Write  six  thousand  four  hundred.             6400. 
Name  the  places,  going  from  right  to  left. 
Ans,  Units,  Tens,  Hundreds,  Thousands. 
Eead  and  then  add  the  following  numbers : — 

1024        1031         1059        1400        1099 
2024        3031        4000        5000        1600 


NOTATION,    NUMERATION.  33 

lilSSSON    XXX. 

What  place  denotes  thousands  ? 
Ans.  The  fourth  place. 

How  do  you  write  five  thousands,  nine  hun- 
dreds, seven  tens,  one  unit  ? 

Ans,  5  in  the  fourth  place  denotes  five  thou- 
sands ;  9  in  the  third  place,  nine  hundreds ;  7 
in  the  second  place,  seven  tens ;  1  in  the  first 
place,  one  unit.    Thus  we  get  5971. 

Eead  this  number. 

Ans.  Five  thousand  nine  hundred  and  seventy- 
one. 

Write  the  following,  placing  units  under  units, 
tens  under  tens,  &c. :  Four  thousands,  8  hun- 
dreds, 6  tens,  2  units ;  five  thousands,  3  hun- 
dreds, 1  ten,  1  unit ;  nine  thousands,  2  hundreds, 
8  tens,  7  units  ;  seven  thousands,  4  hundreds. 

Eead  the  numbers  just  written. 

Mention  the  thousands,  hundreds,  tens,  and 
units,  in  the  following  numbers : — 4629 ;  9780 ; 
5111 ;  1236  ;  7405 ;  2293  ;  529  ;  18. 

When  a  naught  stands  in  the  third  or  second 
place,  must  you  say  no  hundreds,  no  tens  f 

Ans.  No ;  it  is  passed  over  in  reading.  Thus, 
9007  is  read  nine  thousand  and  seven. 

Eead  7012;  6099;  3003;  8064;  1011;  5002. 


34:  NOTATION,    NUMERATION,    COUNTING. 

LESSON    XXXI. 

Write  the  following  numbers  with  figures  : — 
One  thousand  six  hundred  and  fifty-three. 
Five  thousand  nine  hundred  and  eighteen. 
Seven  thousand  eight  hundred  and  ninety. 
Three  thousand  five  hundred  and  seven. 
Eight  thousand  and  forty-nine. 
Eead  the  following  numbers  : — 1321 ;  2906  ; 
6870;  5012;  1864;  9990;  1007;  8700;  3401. 

When  we  count,  one^  two^  three^  four^  &e., 
how  do  we  get  each  number  ? 

Ans,  By  adding  1  to  the  number  going  before. 
Now  in  stead  of  adding  1,  add  2  each  time : 

1  7        13        19        25  31  37 

3  9        15        21        27  33  39 

5        11        17        23        29  35  41 

and  so  on  to  99. 

In  adding  units,  if  the  sum  is  9,  what  do  we  do  ? 

Arts.  We  write  the  9  in  the  units'  place. 

If  the  sum  is  10,  what  do  we  do  ? 

Ans,  10  consists  of  0  units,  1  ten.  6 
Hence  we  write  0  in  the  first  or  units'  place,  _^ 
and  1  in  the  second  or  tens'  place.  10 

Whenever  the  sum  consists  of  two  figures,  how 
must  we  place  them  ? 

Ans,  Set  the  right-hand  figure  in  the  units' 
place,  the  left-hand  figure  in  the  tens'  place. 


ADDITION.  36 


LESSON    XXXII. 

Add  the  following  numbers  : — 

(1)  (2)  (3)  (4)  (5)  (6)  (7) 

4        5  8        7  9        4        9 

3        4  13  111 

2        3  4        2  2        11 

12  3        4  5        6        7 

26  Now  suppose  we  have  to  add  26  and  17. 

17  Begin  at  the  right.  7  and  6  are  13 — three 
43  units  and  1  ten.  We  write  3  in  the  units' 
place,  and  as  there  are  other  tens  we  add 
the  1  ten  in  with  them,  making  4,  which  we 
write  in  the  tens'  place.     Answer,  43. 

"When  the  sum  of  a  column  consists  of  two 
figures,  which  figure  must  we  write  under  the 
column  added  ? 

Ans,  The  right-hand  figure. 

"What  must  we  do  with  the  left-hand  figure  ? 

Ans.  We  must  add  the  left-hand  figure  to  the 
next  column. 

What  if  thel*e  are  no  more  columns  to  be 
added  ? 

Ans.  Then  we  must  write  the  left-hand  figure 
in  the  sum,  in  the  next  place  on  the  left. 

What  do  you  write  down,  and  what  do  you 
add  to  the  next  column,  if  the  sum  of  a  column  is 
96?    Ifitis71;  80;  52;  11;  48;  84:;  17? 


36  ADDING   COLUMNS   ALOUD. 

IiSSSON    XXXIII. 

Look  at  tins  example.     Learn  to  add  eacli 
column  aloud,  in  the  following  manner: — 

1959  1st  column. — Two^  jive^  six^  eighty  sev- 

1032    enteen — write  down  7,  and  add  1  to  the 
c^c^^o    ^6xt  column. 
1342  ^^  column. — One,  jwe,  seven,  ten,  Jlf- 

teen — write  down  5,  and  add  1  to  the  next 

^^^"^    column. 

3d  column. — One,  four,  six,  nine,  eighteen — 
write  down  8,  and  add  1  to  the  next  column. 

4:TH  column. — One,   iAJOo,  four,  seven,  eight, 
nine — write  it  down.    Answer,  9857. 

Add  the  following  in  the  same  way,  not  on 
the  slate,  but  aloud. 


(1) 

(2) 

(3) 

(4) 

(S) 

112 

1270 

1492 

1666 

374 

22 

321 

2101 

1022 

311 

332 

2011 

2121 

232 

1002 

232 

3322 

1060 

2432 

2123 

211 

1346 

2714 

4212 

5463 

909        8270        9488        9564        9273 

Commencing  with  2,  give  the  numbers  formed 
by  adding  2  each  time,  up  to  100.     Thus  : — 

2        6        10        14        18        22        26 

4        8        12        16        20        24        28,  &c. 


ADDING   THREE.  37 


LESSON  XZXIV. 

Add  the  following  numbers.  When  the  left- 
hand  figure  of  any  sum  is  to  be  added  to  the  next 
column,  write  it  in  the  space  under  the  column. 

(1)  (2)  (3)  (4) 

1228  3222  1252  2122 

1654  222  2202  1422 

2343  2222  1942  1465 

3421  3965  2749  4358 


How  much  are  3  and  3  ?  3  and  13  ? 
How  much  are  3  and  4?  3  and  34  ? 
How  much  are  3  and  5  ?  3  and  45  ? 
How  much  are  3  and  6  ?  3  and  66  ? 
How  much  are  3  and  7?  3  and  87? 
Which  is  greater,  900  or  700  ?  900  or  1000  ? 
Which  is  greater,  1  hundred  or  1  thousand  ? 

Commencing  with  3,  give  the  numbers  formed 
by  adding  3  each  time : — 

3  18  33  48 

6  21  36  51 

9  24  39  54 

12  27  42  57 

15  30  45  60 

If  I  have  27  roses,  and  buy  3  more,  how  many 
will  I  then  have  ?  If  some  one  gives  me  three 
more,  and  I  raise  3  from  slips,  how  many  will  I 
then  have  in  all  ? 


63 

78 

93 

66 

81 

96 

69 

84 

99 

72 

87 

102 

75 

90 

105 

38 


ADDING  FOUR. 


LESSON    XXXV. 

How  many  are  4  and  4  ?  4  and  14  ?  4  and 
24?  4and34?  4and44?  4and54?  4and64? 
How  many  are  4  and  5  ?  4  and  75  ?  4  and  85  ? 
How  many  are  4  and  6  ?  4  and  86?  4  and  96? 
How  many  are  4  and  7?    4  and  47?  4  and  67? 


Robert  has  8  fish  in  his  basket  and  4  on  the 
grass ;  how  many  has  he  in  all  ?  How  many 
are  8  and  4?     18  and  4?     28  and  4?     48  and  4? 

How  many  are  4  and  9?  4and89?   34and9? 


Commencing 

witli  4, 

give  the  numbers  formed  J 

by  adding  4  each  time. 

Thus:- 

— 

4 

20 

36 

52 

68 

84 

8 

24 

40 

56 

72 

88 

12 

28 

44 

60 

76 

92 

16 

32 

48 

64 

80 

96 

ADDING  FIVE.  39 


LESSON    XXXVI. 

How  many  are  5  and  5  ?  5  and  15  ?  5  and 
25  ?     5  and  45  ? 

How  many  are  5  and  6  ?  5  and  26  ?     5  and 

36  ?  5  and  46?  5  and  56  ?  55  and  6  ?  5  and 
66  ?     65  and  6  ? 

How  many  are  5  and  7  ?  5  and  77  ? 

How  many  are  5  and  8  ?  5  and  88  ? 

How  many  are  5  and  9  ?  5  and  29  ?  25  and 
9?    5  and  49?    45  and  9?    5  and  59  ?    5and69? 

Commencing  with  5,  give  the  numbers  formed 
by  adding  5  each  time.     Thus  : — 

5  20  35  50  65  80  95 
10  25  40  55  70  85  100 
15        30        45        60        75        90      105 

What  do  these  numbers  end  in  ? 


1.  John  had  twenty  cents ;  his  mother  gave 
him  five,  and  his  father  five  more.  How  many 
had  he  then?     How  many  are  20,  5,  and  5  ? 

2.  Forty-eight  apples  in  one  basket,  and  five 
in  another,  make  how  many  apples  in  all  ? 

3.  A  traveller  rode  thirty-nine  miles  one  day, 
and  five  miles  the  next.  How  far  did  he  ride 
both  days  ?     Add  39  and  5. 

4.  I  have  just  found  five  pins,  said  Eli,  and  I 
had  seventeen  before.     How  many  have  I  now  ? 


40  ADDITION. 


LESSON    XZXVII. 

How  many  are  6  and  6?  6  and  16  ?  46  and  6  ? 
How  many  are  6  and  7  ?     6  and  27  ?     27  and  6  ? 

How  many  are  6  and  8  ?  6  and  88  ?  38  and 
6  ?  58  and  6  ?  How  many  are  6  and  9  ?  6  and 
99?    29  and  6? 

How  many  are  7  and  7  ?  7  and  47  ?  87  and 
7?  How  many  are  7  and  8?  7  and  58?  28 
and  7  ?    How  many  are  7  and  9  ?     69  and  7  ? 

How  many  are  8  and  8  ?  8  and  78  ?  18  and 
8?  How  many  are  8  and  9  ?  8  and  99?  68 
and  9  ?     69  and  8  ? 

How  many  are  9  and  9  ?   9  and  59?  79  and  9? 

How  many  are  10  and  2  ?  40  and  2  ?  6  and 
10  ?  6  and  60  ?  10  and  8  ?  90  and  8  ?  10  and 
9  ?     9  and  100  ?     30  and  3  ? 


1.  There  are  twenty-nine  girls  in  one  class, 
and  eight  in  another ;  how  many  in  both  ? 

2.  How  many  apple-trees  have  I  on  my  farm, 
if  there  are  27  in  one  field  and  6  in  another  ? 

3.  A  half  dollar  is  worth  fifty  cents,  and  a 
dime  ten  cents.     How  much  are  both  worth  ? 

4.  Nine  pigeons  join  a  flock  of  thirty-eight. 
How  many  does  the  flock  then  contain  ? 

5.  Sixteen  roses  in  one  bouquet,  and  eight  in 
another,  make  how  many  in  both  ? 


EXAMPLES   IN   ADDITION.  41 

LESSON    XXXVIII. 

Eead  the  following  numbers  in  turn.     Add 
aloud  (not  on  the  slate),  as  shown  on  page  36. 


(1) 

(2) 

(3) 

(4) 

546 

145 

834 

689 

8063 

2083 

1045 

1989 

789 

1978 

626 

3754 

4261 

939 

3997 

1965 

825 

1987 

1698 

876 

94:84  7132  8200  9273 

Some  examples  for  the  slate  follow.  Be  sure 
to  set  units  under  units,  tens  under  tens,  &c. 

1.  Add  ninety-nine  ;  eighty-seven  ;  fifty-six ; 
twenty-four  ;  and  one  hundred  and  eight. 

2.  Add  four  hundred  and  fifty ;  nineteen  ; 
eight  thousand  six  hundred  and  nine ;  seven  hun- 
dred and  twenty-three  ;  and  eighty-four. 

3.  Add  two  thousand  four  hundred  and 
twenty-one ;  nine  hundred  and  eighty-seven ; 
eighteen  hundred  and  ninety-nine ;  three  thou- 
sand and  sixteen ;  nine  hundred  and  ninety-nine. 

4.  Add  three  thousand  and  eight ;  nine  hun- 
dred and  ninety ;  seventeen  hundred  and  fifty-six  ; 
five  hundred  and  ninety-seven;  two  thousand 
eight  hundred  and  eighty-eight. 

What  is  Numeration?  What  is  Notation? 
What  is  Addition  ? 


42 


SUBTEACTION. 


LESSON    XXZIZ. 

Two    pigeons    were    on    the 

ground.     One  has  flown  away ; 

how  many  are  left  ? 

Two  cows  were  standing 

near  a  pond.  One  of  them  has 

gone  into   the  water ;   how 


many  are  left  on  the  bank  ? 

Take  1  from  2,  and  what  is  left 

What  is  this  process  called  ? 

Ans,  Subtraction. 

What  is  Subtraction  ? 

Ans,  Subtraction  is  the  process  of  taking  one 
number  from  another. 

When  we  count  one,  two,  three,  four,  &c., 
how  do  we  get  each  number  ? 

Ans,  By  adding  1  to  the  number  going  before. 

When  we  count  backward,  ten,  nine,  eight, 
&c.,  how  do  we  get  each  number  ? 

Ans,  By  subtracting  1  each  time  from  the 
number  going  before. 

Count  backward  from  100  to  1. 


from  1  leaves  0. 
from  2  leaves  1. 
from  3  leaves  2. 
from  4  leaves  3. 
from  5  leaves  4. 


from 
from 
from 
from 
from 


6  leaves  5. 

7  leaves  6. 

8  leaves  7. 

9  leaves  8. 
10  leaves  9. 


SXJBTKACTION. 


43 


LESSON   XL. 

What  is  Subtraction  ? 

When  we  take  one  number  from   another, 
what  is  the  result  called  ? 
Arts,  The  Remainder. 


Three  boys  were  riding.  Two  got  out  to 
gather  berries ;  how  many  were  left  in  the  wagon  ? 

Four  dogs  ran  barking  after  the  wagon.  Two 
have  turned  back  ;  how  many  are  lef^  there  ? 

Five  cows  were  standing  in  a  field.  Two  have 
lain  down ;  how  many  remain  standing  ? 


2  from  2  leaves  0. 
2  from  3  leaves  1. 
2  from  4  leaves  2. 
2  from  5  leaves  3. 
2  from  6  leaves  4. 


2  from     7  leaves  5. 

2  from     8  leaves  6. 

2  from     9  leaves  7, 

2  from  10  leaves  8. 

2  from  11  leaves  9. 


44  QUESTIONS   IN   SUBTRACTION. 

LESSON    XLI. 

Which  of  two  numbers  must  we  take  from 
the  other,  to  find  their  difference  ? 

Ans,  We  must  take  the  less  from  the  greater. 


1.  Susan  has  six  apples,  and  gives  away  two  ; 
how  many  has  she  left  ? 

2.  If  John  has  ten  marbles,  and  loses  one, 
how  many  has  he  then  ? 

3.  A  man  having  five  sheep,  sold  one ;  how 
many  remained  unsold  ? 

4.  Mary  gives  a  beggar  two  cakes.  She  had 
nine  before ;  how  many  has  she  left  ? 

5.  If  there  are  two  boys  in  a  class  of  seven 
children,  how  many  girls  are  in  the  class  ? 

6.  2  from  4  leaves  how  many  ?  2  from  24  ? 
2  from  54  ?     2  from  74  2 

7.  Two  from  6,  how  many  ?    2  from  96  ? 

8.  Two  from  8,  how  many  ?  2  from  48  ?  2 
from  78  ?     2  from  38  ? 

Commencing  with  50,  give  the  numbers  ob- 
tained by  subtracting  2  each  time.  Thus :  60, 
48,  46,  44,  42,  40,  38,  36,  34,  32,  30,  &c. 

EXAMPLES  EOB  THE   SLATE, 
(1)  (2)  (3)  (4)  (5) 

From  98    891    437   1652    7234 
Take  12    120    121    212    2112 

Remainder 


SUBTRACTION. 


45 


LESSON   ZLII. 

What  is   Subtraction  ?    What  is  the  result 
obtained  by  Subtraction  called  ? 


There  are  4  panes  of  glass  in  this  barn  win- 
dow.    If  3  are  broken,  how  many  are  unbroken  ? 

There  were  five  sheep  in  the  barn-yard,  but 
three  have  gone  into  the  field.  How  many 
remain  ?     Count  them  in  the  picture. 

Nine  chickens  were  on  the  ground ;  3  have 
gone  to  roost.    How  many  are  left  on  the  ground  ? 


from 
from 
from 


3  leaves  0. 

4  leaves  1. 

5  leaves  2. 


from  6  leaves  3. 
from  7  leaves  4. 


3  from  8  leaves  5. 
3  from  9  leaves  6. 
3  from  10  leaves  7. 
3  from  11  leaves  8. 
3  from  12  leaves  9. 


46 


SUBTRACTION". 


LESSON    XLIII. 

Take  four  oxen  from 
four  oxen,  and  how  many- 
are  left  ?  Cover  four  over, 
and  count  the  rest. 

Take  four  eggs  from  a  nest  con- 
taining five,  and  how  many  remain  ? 
Cover  4,  and  count  the  rest. 

Here  is  a  knife  with  six  blades. 
If  4  of  them  are  closed,  how  many 
are  open  ?  4  from  6  leaves  how  many  ? 

Here  are  seven  flowers  on  one 
stem,  but  four  are  broken ;  how  many 
are  unbroken  ? 

-X-X-X-X-    -X--X-X-X-    From  eight  stars  take 
four  stars  ;  how  many  are  left  ? 

A  lady  having  nine 
wine  glasses,  broke  four 
of  them ;  how  many  had  she  left  ? 

Four  from  ten  leaves  how  many  ? 


iIitailJLiXiidL4L 


4  from  4  leaves  0. 
4  from  5  leaves  1. 
4  from  6  leaves  2. 
4  from  7  leaves  3. 
4  from  8  leaves  4. 


4  from    9  leaves  5. 

4  from  10  leaves  6. 

4  from  11  leaves  7. 

4  from  12  leaves  8. 

4  from  13  leaves  9. 


QUESTIONS   IK  SUBTKACTION.  47 

LESSON   XLIV. 

1.  Three  from  7  leaves  how  many?  3  from 
17?  3  from  37?  3  from  67?  Three  from'  8 
leaves  how  many  ?  3  from  88  ?  3  from  98  ?  3 
from  28  ? 

2.  Three  from  9  leaves  how  many  ?   3  from  79? 

3.  Three  from  ten  leaves  how  many  ?  Three 
from  twenty  ?   3  from  30  ?   3  from  40  ?  3  from  50  ? 

4.  Commencing  with  60,  give  the  numbers 
obtained  by  subtracting  3  each  time.  Thus  :  60, 
57,  64,  51,  48,  45,  42,  39,  &c. 

5.  Twelve  things  make  a  dozen.  If  Jane 
buys  a  dozen  needles,  and  gives  away  3,  how 
many  does  she  keep  ?  If  she  loses  3  of  these, 
how  many  has  she  then  ? 

6.  A  boy  spends  four  cents ;  how  much  has 
he  left,  if  he  had  twelve  cents  at  first  ? 

7.  Amy  is  four  years  younger  than  Lucy,  and 
Lucy  is  13  ;  how  old  is  Amy  ? 

8.  If  there  are  eleven  persons  in  an  omnibus, 
and  three  get  out,  how  many  remain  ?  If  four 
more  get  out,  how  many  then  are  left  ? 

Eead  these  numbers.  Write  them  down  on 
your  slate.     Subtract,  and  read  the  remainders. 

(9)  (10)  (11)  (12)  (13) 

From  647    983    1085    4293    7658 
Take  434    423    1043    4131    3343 


48 


SUBTEACTION. 


LESSON    XLV. 

Is  4:  greater  or  less  than  5  ?     |  |  |  |    |  |  |  1 1 
Can  we  subtract  five  from  four  ? 
Can  we  subtract  five  from  five  ? 

If  we  take  five  dolls  away 
from  five  dolls,  bow  many  are 
left  ?     Try  and  see. 

Whenever  we  subtract  a  number  from  itself, 
as  5  from  5,  what  is  the  remainder  ? 
Ans,  Nothing,  or  naught — 0. 

\jjf  Njjt        Five  marks  from  ten  marks  leave 
I  In     I  In  ]^q^  many  marks  ?      Cover  five,  and 
count  the  rest. 

Five  marks    from    twenty  marks 
leave  how  many  marks  ? 

Five  from  thirty  leaves  how  many  ?     [jjj  "^Hjj 
5  from  40  ?     6  from  50  ?     5  from  60  % 


^IHJ 


James  had  6  books  on  his  table ; 
5  have  fallen  down.  How  many 
are  left  on  the  table  ? 


5  leaves  0. 

6  leaves  1. 

7  leaves  2. 
from  8  leaves  3. 
from  9  leaves  4. 


from 
from 
from 


from  10  leaves 
from  11  leaves 
from  12  leaves 
from  13  leaves 
from  14  leaves 


QUESTIONS   IN   SUBTEACTIOlSr.  49 


LESSON    XLVI. 

1.  Thirteen  persons  were  dining  together. 
Four  got  up  and  left ;  how  many  remained  ? 

2.  Maud  is  seven  years  old ;  her  brother,  is 
five.     Which  is  the  older,  and  how  much  ? 

3.  A  man  who  had  fourteen  cents  in  his 
pocket,  gave  away  all  but  five  to  beggars.  How 
much  did  he  give  away  ? 

4.  Twelve  persons  were  standing  near  a  boiler 
which  burst.  Two  were  killed,  and  three  were 
injured ;  how  many  were  unhurt  ? 

5.  If  I  borrow  eleven  dollars,  and  pay  back 
four,  how  many  do  I  owe  ? 

6.  Five  from  eight  leaves  how  many  ?  5  from 
18  ?     5  from  28  ?     5  from  38  ?     5  from  48  ? 

7.  Five  from  nine  leaves  how  many  ?  5  from 
69  ?     5  from  89  ?     5  from  79  ?     5  from  99  ? 

8.  K  a  boy  who  has  thirty-seven  hens,  sells 
four,  how  many  has  he  left  ? 

9.  A  certain  boat  holds  19  persons.  If  five 
are  in  it,  how  many  empty  seats  are  there  ? 

10.  Five  from  10  leaves  how  many  ?   5  from  5  ? 

EXAMPLES   FOR   THE   SLATE, 
(1)  (2)  (3)  (4)  (5) 

From  937    8165    4397    6028    5984 
Take  425    5054    2154    4014    5234 


50 


SUBTKACTION'. 


LESSON    XLVII. 

What  is  the  smallest  number  that  we  can 
subtract  6  from  ? 

How  many  does  6  from  6  leave  ? 

Look  at  these  seven  mice.  Six 
are  running  away;  how  many 
remain  ?  ^ 

Six  from  7  leaves  how  many?     6  from  17? 
6  from  27  ?    6  from  47  ?    6  from  67  ? 

This  wheel  has  eight  spokes.     Six  of 
them  are  whole  ;  how  many  are  broken  I 
Count  and  see. 
Six  from  8  leaves  how  many  ?     6  from  38  ? 
6  from  58  ?     6  from  78  ?     6  from  98  ? 

Take  six  forks  away  from  nine 
forks,  and  how  many  are  left  ? 

^wC^c^r   ^c  /\  7r^r^r^\     >^-»^-^  stars  irom  len 
stars  leave  how  many  stars  ? 

1 1  I  I  I    I  I  I  I  I  I     Six  marks  from  eleven  marks 
leave  how  many  marks  ? 


6  leaves  0. 

7  leaves  1. 

8  leaves  2. 

9  leaves  3. 


6  from 
6  from 
6  from 
6  from 
6  from  10  leaves  4. 


6  from  11  leaves  5 

6  from  12  leaves  6. 

6  from  13  leaves  7 

6  from  14  leaves  8 

6  from  15  leaves  9. 


SUBTEACTION. 


51 


LESSON    XLVIII. 

What  is  Subtraction?  What  is  the  answer 
to  a  question  in  Subtraction  called  ? 

What  is  the  smallest  number  that  we  can 
subtract  7  from  ? 

How  many  does  seven  from  seven  leave  ?  7 
from  27  ?    7  from  97  ?    7  from  57  ?    7  from  37  ? 

Eight  fingers  on  two  hands.     If 

seven  of  them  are  held  up  straight, 

how  many  will  be  bent  down  ? 

How  many  does  seven  from  eight  leave  ?     7 

from  18  ?    7  from  88  ?     7  from  68  ?     7  from  48  ? 

7  from  58? 

Here  we  have  nine  rin^s  '"n  A  n  A  A  n  A  A  A'" 
onastrbg.     If  you  cover  ^'J  "  ^  ^  "  U  U  U 

7  with  your  hand,  how  many  will  you  see  ? 

Seven  from  9  leaves  how  many  ?     7  from  79  ? 
Ten  bees  are  flying  round  a  hive. 
If  7  are  on  one  side,  how  many  are 
on  the  other  ?     Count  and  see. 
Seven  from  ten  leaves  how  many  ? 


7  from  7  leaves  0. 
7  from  8  leaves  1. 
7  from  9  leaves  2. 
7  from  10  leaves  3. 
7  from  11  leaves  4. 


7  from  12  leaves 
7  from  13  leaves 
7  from  14  leaves 
7  from  15  leaves 
7  from  16  leaves 


62  QUESTIONS   IN   SUBTRACTION. 

IiESSON    XLIX. 

1.  There  were  thirteen  lights  in  a  street.  Six 
are  blown  ont ;  how  many  are  left  burning  ? 

2.  Henry  broke  7  teeth  ont  of  a  comb. 
How  many  teeth  were  left,  if  there  were  27  at 
first? 

3.  How  many  sngar-plums  wonld  you  have 
to  put  with  nine,  in  order  to  make  fifteen  ? 

4.  If  a  boy  has  eleven  almonds,  and  eats  all 
but  seven,  how  many  does  he  eat  ? 

5.  A  blind  man  received  eight  cents  from  one 
kind  boy,  and  four  from  another.  If  he  spent 
six  cents  on  his  way  home,  how  many  had  he 
left? 

EXAMPLES    FOB   THE    SLATE. 

1.  From  ninety-seven  subtract  seventy-six. 

2.  Take  six  thousand  and  seventeen  from 
eight  thousand  three  hundred  and  forty-eight  ? 

3.  From  five  thousand  and  seventy-two  take 
three  thousand  and  twenty-two. 

4.  A  man  having  ninety-one  dollars,  bought 
a  coat  for  twenty  dollars ;  how  much  had  he  left? 

5.  A  ship  with  six  hundred  and  sixty-nine 
passengers  on  board  was  wrecked.  Four  hundred 
and  sixteen  escaped ;  how  many  were  lost  ? 

6.  A  gale  swept  over  a  garden  containing 
eighty-seven  bean-poles.  Seventy-six  were  blown 
down ;  how  many  remained  standing  ? 


SUBTRACTION'. 


63 


LESSON    L. 

What  is  the  smallest  number  that  we  can  take 
8  from? 

How  many  does  eight  from  eight  leave?     8 

from  108  ?     8  from  68  ?     8  from  18  ?     8  from  58  ? 

Nine  marbles  were  placed  in 

the  centre  of  a  ring.     The  first 

boy  that  shot,  drove  eight  away 

from  the  centre ;  how  many  were 

left  there? 

8  from  9  leaves  how  many  ?     8  from  29  ? 

Ten  trees  were  set  out  thus.     If    o     o     o     o 
8  afterwards  died,  how  many  re-      ©  o 

mained  ?     Cover  8  over,  and  count    o     o     o     o 
the  rest.     8  from  10  leaves  — . 

Eleven  spiders  were  on  a  wall, 
but  eight  have  crawled  down. 
How  many  remain  there  ?  8  from 
11  leaves  how  many  ? 

Take  eight  rings  ^^  ^^^^ 
from  twelve  rings,  and  how  many  q  q  o  o  o  o 
will  be  left? 


8  from 

8  from 

8  from  10  leaves 

8  from  11 


8  leaves  0. 

9  leaves  1. 
2. 

leaves  3. 


8  from  12  leaves  4. 


8  from  13  leaves 
8  from  14  leaves 
8  from  15  leaves 
8  from  16  leaves 
8  from  17  leaves 


54 


SUBTRACTION. 


LESSON     III. 


Here  is  a  frame  with  wires  stretched  across 
it,  and  each  wire  runs  through  balls. 

Count  the  balls  on  the  top  wire.  How  many 
are  there  in  all  ?  Now,  if  from  these  10  balls, 
we  push  away  9  to  the  right,  how  many  are  left  ? 

How  many  balls  on  the  second  wire  ?  Push 
away  9,  and  how  many  are  left  ? 

How  many  balls  on  the  third  wire  ?  Cover 
9  with  your  finger,  and  how  many  do  you  see  ? 

How  many  balls  on  the  fourth  wire  ?  Cover 
9  over,  and  how  many  can  you  count  ? 

How  many  balls  on  the  fifth  wire?  Cover 
9  over,  and  how  many  are  left  ? 


9  from  9  leaves  0. 
9  from  10  leaves  1. 
9  from  11  leaves  2. 
9  from  12  leaves  3. 
9  from  13  leaves  4. 


9  from  14  leaves  5. 
9  from  15  leaves  6. 
9  from  16  leaves  7. 
9  from  17  leaves  8. 
9  from  18  leaves  9. 


QUESTIONS   IN   SUBTEACTION,  55 


LESSON  LII. 

1.  A  jar  of  lard  weighed  seventeen  pounds. 
If  the  jar  weighed  eight  pounds,  what  was  the 
weight  of  the  lard  ? 

2.  I  bought  a  dozen  eggs,  but  eight  of  them 
were  bad.     How  many  were  good  ? 

3.  Sixteen  boys  went  a  skating.  If  nine  of 
them  fell  on  the  ice,  how  many  escaped  falling  ? 

4.  A  farmer  had  eighteen  cows.  Four  of 
them  died,  and  he  sold  five  ;  how  many  were  left? 

5.  Nine  lemons  fell  from  a  tree  on  which 
thirteen  were  growing.     How  many  remained  ? 

6.  A  fisherman  who  had  seventeen  lobsters, 
sold  six  in  the  morning  and  two  in  the  afternoon. 
How  many  had  he  left  ? 

7.  A  boy  having  fourteen  dollars  in  the  bank, 
drew  out  all  but  eight.  How  much  did  he  draw 
out? 

EXAMPLES    FOR  THE   SLATE. 
(1)  (2)  (3)  (4)  (5) 

From  18    873    5268    9145    8460 
Take  9    721    1045    8043    6250 


(6)       (7)        (8)        (9)        (10) 

From  17    921    2397    5679    4396 
Take  8    721    1163    4645    3291 


56  SUBTE  ACTION. 


LESSON    LIII. 

From      652 
Take       379 


Look  at  this  example.  The  lower  number  is 
the  smaller ;  hence  it  can  be  taken  from  the  upper. 

Always  begin  to  subtract  at  the  right, 

9  from  2. — We  can  not  take  9  from  2,  because 
9  is  greater  than  2.  So  we  add  10  to  the  2, 
making  it  12.  9  from  12  leaves  3.  Write  down  3 
for  the  first  figure  of  the  remainder. 

Now,  to  balance  the  10  units  just  added  to  3 
in  the  upper  line,  add  1  ten  to  the  7  tens  in  the 
lower  line, — making  8.     Subtract  8. 

8  from  5. — ^We  can  not  take  8  from  5.  So 
add  10  to  the  5,  making  it  15.  8  from  15  leaves 
7.  Write  down  7  for  the  second  figure  of  the  re- 
mainder. 

To  balance  the  10  just  added  to  the  5  tens  in 
the  upper  line,  add  1  hundred  to  the  3  hundreds 
in  the  lower  line, — making  4.     Subtract  4. 

4  from  6  leaves  2.  Write  down  2  for  the  third 
figure  of  the  remainder.     Answer,  273. 

How,  then,  are  we  to  proceed,  when  the  lower 
figure  is  greater  than  the  one  above  it  ? 

Ans.  When  the  lower  figure  is  greater  than  the 
one  above  it^  we  add  10  to  the  upper  fi^gure^  sub- 
tract^ am^d  then  add  1  to  the  next  lower  figure. 


QUESTIONS   IN   SUBTRACTION^.  57 


LESSON    LIV. 

EXAMPLES    FOR  THE    SLATE. 
(1)  (2)  (3)  (4)  (5) 

From  752    8364    9017    3429    8560 
Take  479    2192    4108    3173    6936 


(6)  (7)  (8)  (9)  (10) 

From  416        5832        7411        8267        6059 
Take  273         1988        4143         3479         3421 


11.  There  were  seven  hundred  and  live  fish 
in  a  net.  But,  in  drawing  the  net,  ninety-six 
were  lost ;  how  many  fish  were  caught  ? 

12.  Charles  bought  some  meat  for  thirty-nine 
cents.  He  gave  the  butcher  half  a  dollar  (worth 
fifty  cents).     How  much  change  did  he  get  ? 

13.  A  man  who  had  four  thousand  and  ten 
dollars,  gave  his  son  two  thousand  seven  hundred 
and  eight  dollars.     How  much  did  he  keep  ? 

14.  A  farmer  sold  eight  hundred  and  twenty- 
five  acres  of  land.  How  many  had  he  left,  if  his- 
farm  contained  a  thousand  acres  at  first  ? 

15.  Fanny  had  a  present  of  a  box  containing 
144  pens.  If  she  used  thirty-nine  of  them  in  a 
month,  how  many  had  she  left  ? 

16.  A  drover  sold  87  head  of  cattle  out  of  a 
drove  of  250.     How  many  had  he  left  ? 


58  EXERCISE   IN   SUBTRACTION. 

LESSON    LV. 

MENTAL   EXERCISES. 

1.  A  car  started  with  40  passengers.  At  tlie 
first  station,  10  passengers  got  off  and  3  got  on. 
How  many  did  it  then  contain  ? 

2.  A  rose-bush  had  82  roses  on  it.  The  next 
day,  6  of  these  roses  fell  to  pieces,  and  9  new  ones 
opened.     How  many  were  then  on  the  bush  ? 

3.  Leaving  home  with  a  hundred  dollars  in 
my  purse,  I  spent  five  for  a  vest,  five  for  a  coat, 
and  five  for  boots.     How  much  had  I  left  ? 

4.  Said  Dick  to  Stephen,  "  Give  me  your  nine 
chickens,  and  I  shall  have  seventy-eight."  How 
many  chickens  had  Dick  ? 

5.  A  man  rode  90  miles  in  4  days.  The  first 
day  he  went  70  miles ;  the  second  day,  10 ;  the 
third  day,  5.     How  far  did  he  go  the  fourth  day  ? 

6.  Subtract  the  sum  of  70, 10,  and  5,  from  90. 

7.  If  Julia  is  twenty-three  years  old,  and  her 
brother  is  twenty-nine,  what  is  the  difference  in 
their  ages  ? 

8.  Six,  and  five,  and  nine,  and  how  many 
more,  make  twenty-eight  ? 

9.  A  man  who  had  twenty  cents,  met  five  poor 
boys,  and  gave  them  each  three  cents.  How 
many  cents  had  he  left  ? 

10.  From  20  take  the  sum  of  3,  3,  3,  3,  and  3. 


MULTIPLICATION. 


59 


LESSON   LVI. 

"What  does  once  mean  ?    Arts,  One  time. 

What  does  injoice  mean  ?    Ans,  Two  times. 

One  bird,  taken  once, 
is  one  bird.  Twice  one 
bird  is  bow  many  birds  ? 

Two  birds,  taken 
once,  are  two  birds. 
Twice  two  birds  are  how 
many  birds  % 

"What  is  taking  a  number  one  or  more  times 
called  ? 

Ans.  Multiplying. 

Taking  a  number  once  is  multiplying  by  1. 
Taking  a  number  twice  is  multiplying  by  2. 
Taking  a  number  3  times  is  multiplying  by  3. 

Multiplying  is  a  short  way  of  doing  what  ? 
Ans.  Of  adding  a  number  to  itself.     Thus : — 

Twice  1  is  2.  1  and  1  are  2. 

Three  times  1  is  3.  1  and  1  and  1  are  3. 

When  we  multiply,  what  is  the  result  called  ? 
Ans,  The  Product.     When  we  say  Twice  one 
is  twOy  2  is  the  product. 

What  is  Multiplication  ? 
Ans.  Multiplication  is  the  process  of  taking  a 
number  a  certain  number  of  times. 


60 


MULTIPLICATION. 


Once  2  is  2. 
product  ? 


LESSON    LVII. 

One  swan,  taken  once, 
is  one  swan.  Once  1  is 
1.  If  1  is  multiplied  by 
1,  what  is  the  product  ? 
Two  ducks,  taken 
once,  are  two  ducks. 
If  2  is  multiplied  by  1,  what  is  the 


-/Hwr  How  many  do  three  stars,  taken  once, 
make  ?  How  much  is  once  3  ?  If  3  is  multiplied 
by  1,  what  is  the  product  ? 

How  many  do  four  eggs,  taken 
2^.  once,  make  ?    How  much  is  once  4  ? 
If  4  is  multiplied  by  1,  what  is  the 
product  ? 

Then,  Once  1  is  1.  Once  2  is  2.  Once  3  is 
3.  Once  4  is  4.  Once  any  number  is  the  number 
itself. 

Learn  the  Table  forward  and  backward. 


Once  1  is  1. 

Once    6  is 

6 

Once  2  is  2. 

Once    7  is 

7 

Odcc  3  is  3. 

Once     8  is 

8 

Once  4  is  4. 

Once     9  is 

9 

Once  5  is  5. 

Once  10  is 

10 

MULTIPLICATION. 


61 


LESSON    LVIII. 


EXAMPLES   FOB  THE   SLATE. 


(1) 

^2) 

(3) 

(*) 

(S) 

Multiply 

98 

150 

742 

3018 

6932 

By 

1 

1 

1 

1 

1 

m      • 

1               • 

one  aeer  is 
how  many  deer  ?  How 
mucli  is  twice  1  ? 

Twice  two  trees  are 
tow  many  trees  ?  How 
mucli  is  twice  2  ? 


\r   \r   x/ 


Twice  three  stars  are  how  many  stars  ? 
"/{•■/(-"/r   How  much  is  twice  3  ? 

What  is  the  same  as  multiplying  a  number 
by  2? 

Ans,  Adding  the  number  to  itself. 

Twice  1  is  2.  1  and  1  are  2. 

Twice  2  is  4.  2  and  2  are  4. 


Twice  1  is    2. 

Twice     6  is  12. 

Twice  2  is    4. 

Twice    7  is  14. 

Twice  3  is    6. 

Twice    8  is  16. 

Twice  4  is     8. 

Twice    9  is  18. 

Twice  5  is  10. 

Twice  10  is  20. 

62  MULTIPLICATION. 


LESSON    LIX. 

0,  taken  any  number  of  times,  is  still  0. 
Twice  0  is  0.     3  times  0  is  0.     4  times  0  is  Go 

Now  you  have  some  examples  for  the  felate. 
Read  the  numbers  multiplied,  and  the  products. 


(1) 

(2) 

(3) 

(*) 

(S) 

Multiply    34 

121 

620 

4213 

3004 

By                2 

2 

2 

2 

2 

6.  How  much  is  twice  four  hundred  and  three  ? 

7.  Multiply  two  thousand  one  hundred  and 
eleven  by  two. 

8.  If  two  thousand  three  hundred  and  forty 
one  is  multiplied  by  two,  what  is  the  product  ? 

9.  How  much  is  once  seventy-six  ? 

10.  Multiply  four  thousand  and  thirteen  by  2, 

11.  What  is  the  product  of  one  and  two  thou- 
sand seven  hundred  ? 

12.  How  much  is  twice  five  hundred  and 
thirty-two  ? 

13.  Multiply  twelve  hundred  by  two. 


3  times  1  is  3. 
3  times  2  is  6. 
3  times  3  is  9. 
3  times  4  is  12. 
3  times  5  is  15. 


3  times  6  is  18. 

3  times  7  is  21. 

3  times  8  is  24. 

3  times  9  is  27. 

3  times  10  is  30. 


MULTIPLICATION-.  C3 


LESSON    liX. 

1,  If  a  cord  of  wood  costs  five  dollars,  what 
will  three  cords  cost  ? 

Model. — If  1  cord  costs  5  dollars,  3  cords  will  cost  3 
times  5  dollars,  or  15  dollars.    Answer,  15  dollars. 

Follow  this  model  in  all  tlie  mental  exercises  under 
Multiplication. 

2,  What  will  two  books  cost,  at  a  dollar  each  ? 
8.  How  much  will  a  clerk,  who  gets  eight 

dollars  a  week,  earn  in  three  weeks  ? 

4.  At  10  dollars  each,  what  will  2  desks  cost  ? 

5.  A  man  gave  two  beggars  nine  cents  apiece ; 
how  much  did  he  give  them  both  ? 

6.  If  one  woman  can  make  three  dresses  in  a 
week,  how  many  dresses  can  three  women  make  ? 

7.  I  have  two  classes,  each  containing  seven 
boys  ;  how  many  boys  do  both  contain  ? 

8.  If  a  barrel  of  flour  lasts  a  family  nine  weeks, 
how  long  will  three  barrels  last  them  ? 

9.  When  oranges  are  worth  two  cents  apiece, 
and  lemons  one  cent,  what  will  I  have  to  pay  for 
three  oranges  and  two  lemons  ? 


A  times  1  is  4. 
4  times  2  is  8. 
4  times  3  is  12. 
4  times  4  is  16. 
4  times  5  is  20. 


4  times  6  is  24. 
4  times  7  is  28. 
4  times  8  is  32. 
4  times  9  is  36. 
4  times  10  is  40. 


64 


MULTIPLICATION. 


Ht   LXI. 

If  one  girl  can 
pick  five  quarts  of 
berries  in  a  morn- 
ing, how  many 
quarts  can  four 
girls  pick  ? 

2.  There  are  four  fingers  on  one  hand ;  how 
many  are  there  on  four  hands  ? 

3.  How  many  days  are  there  in  four  weeks, 
there  being  seven  days  in  one  week  ? 

4.  What  will  4  combs  cost,  at  10  cents  apiece  ? 

5.  If  one  horse  eats  8  quarts  of  oats  in  a  day, 
how  much  will  4  horses  eat  at  the  same  rate  ? 

6.  A  father  gave  each  of  his  4  sons  3  dollars  ; 
how  much  did  he  give  them  in  all  ? 

7.  If  one  stage  holds  9  men,  how  many  men 
will  4  such  stages  hold  ? 

Commencing  with  5,  give  the  numbers  formed 
by  adding  5  each  time.  Thus :  5,  10,  15,  20,  25, 
30,  &c. 


times  1  is  5. 

times  2  is  10. 

times  3  is  15. 

times  4 


5 
5 
5 
5 

5  times  5 


is  20. 
is  25. 


times 
times 
times 
times 


6  is  30. 

7  is  35. 

8  is  40. 

9  is  45. 


times  10  is  50. 


MITLTIPLICATIOIir.  65 


liESSON    LXII. 

How  much  is  5  times  4  ?  How  much  is  4 
times  5?    Which  is  the  greater? 

How  much  is  5  times  3  ?  How  much  is  3 
times  5  ?    Which  is  the  greater  ? 

In  finding  the  product  of  two  numbers,  does 
it  matter  which  we  multiply  by  ? 

1.  How  many  miles  will  a  horse  trot  in  5 
hours,  if  he  trots  10  miles  an  hour  ? 

2.  If  Henry  reads  5  books  every  week,  how 
many  will  he  read  in  5  weeks  ? 

3.  What  are  5  pounds  of  pork  worth,  at  9 
cents  a  pound  ? 

4.  How  many  trees  are  there  in  5  rows,  con- 
taining 6  trees  each  ? 

5.  Louise  writes  2  pages  every  day ;  how 
many  pages  does  she  write  in  5  days  ? 

6.  There  are  5  cages  in  the  Museum,  with  8 
monkeys  in  each  ;  how  many  monkeys  in  all  ? 

7.  Ned  went  5  times  to  the  station,  and  took 
1  letter  each  time  ;  how  many  did  he  take  in  all  ? 


6  times  1  is  6. 
6  times  2  is  12. 
6  times  3  is  18. 
6  times  4  is  24. 


6  times  6  is  36. 

6  times  7  is  42. 

6  times  8  is  48. 

6  times  9  is  54. 


6  times  5  is  30.     I     6  times  10  is  60. 


66  MULTIPLICATION. 


LESSON   LXIII. 

How  mucli  is  6  times  2  ?    How  mucJb  is  twice 
6  ?    Which  is  greater  ? 

Which  is  greater,  6  times  4  or  5  times  5  ? 
Which  is  greater,  6  times  2  or  3  times  4  ? 

1.  Walking  three  miles  an  hour,  how  far  will 
a  man  go  in  six  hours  ? 

2.  If  one  box  of  tea  lasts  a  family  six  months, 
how  long  will  six  boxes  last  them  ? 

3.  How  many  dollars  are  there  in  six  bags, 
containing  seven  dollars  each  ? 

4.  One  eagle  is  worth  ten  dollars.   How  many 
dollars  are  six  eagles  worth  ? 

5.  How  far  will  we  get  from  Albany,  sailing 
6  hours  in  a  boat  that  goes  9  miles  an  hour  ? 

6.  Jane  and  her  five  sisters  have  each  a  canary 
bird.     How  many  birds  have  they  all  ? 

7.  How  many  flowers  are  there  in  6  nosegays, 
if  each  contains  8  flowers  ? 

8.  Six  pin-cushions,  with  five  pins  in  each, 
will  contain  how  many  pins  in  all  ? 


7  times  1  is  7. 
7  times  2  is  14. 
7  times  3  is  21. 
7  times  4  is  28. 
7  times  5  is  35. 


7  times  6  is  42. 
7  times  7  is  49. 
7  times  8  is  56. 
7  times  9  is  63. 
7  times  10  is  70. 


MULTIPLICATION". 


67 


LESSON    LXIV. 


1.  How  many  panes  of  glass  are  there  in  7 
windows,  containing  8  panes  each  ? 

2.  If  a  boy  spends  four  cents  a  day,  how  mnch 
will  he  spend  in  a  week,  which  contains  7  days  ? 

3.  One  fly  has  two  wings  ;  how  many  wings 
have  seven  flies  ? 

4.  What  will  7  rings  cost,  at  9  dollars  each  ? 

5.  How  many  pages  will  Ella  read  in  seven 
days,  if  she  reads  seven  every  day  ? 

6.  How  many  dollars  in  seven  eagles,  allow- 
ing ten  dollars  to  the  eagle  ? 

7.  How  many  boats  pass  a  draw-bridge  in  7 
days,  if  five  boats  go  through  each  day  ? 


8  times  1  is  8. 
8  times  2  is  16. 
8  times  3  is  24. 
8  times  4  is  32. 
8  times  5  is  40. 


8  times  6  is  48. 
8  times  7  is  56. 
8  times  8  is  64. 
8  times  9  is  72. 
8  times  10  is  80. 


68 


MULTIPLICATION. 


LESSON    LXV. 


1.  If  these  boys  skate  four  miles  an  hour,  how 
many  miles  will  they  skate  in  8  hours  ? 

2.  Twice  every  day  Fred  and  Frank  come 
with  their  sleds,  to  ride  down  hill.  How  many 
times  do  they  come  in  eight  days  ? 

3.  If  it  takes  3  hours  to  cut  a  ton  of  ice  from 
the  pond,  how  long  will  it  take  to  cut  8  tons  ? 

4.  One  day  8  sleigh-loads,  of  9  persons  each, 
came  to  the  pond  ;  how  many  persons  came  ? 

5.  What  will  eight  loads  of  evergreens  cost, 
at  six  dollars  a  load  ? 


9  times 
9  times 
9  times 


1  is    9. 

2  is  18. 

3  is  27. 


9  times  4  is  36. 
9  times  5  is  45. 


9  times 
9  times 
9  times 
9  times 


6  is  54. 

7  is  63. 

8  is  72. 

9  is  81. 


9  times  10  is  90. 


MULTIPLICATION.  69 


LESSON    LXVI. 

(1)               (2)               (3)             (4)  (5)  (6) 

Multiply  41        21        90        81  YO  621 

By           5          6          7          8  9  4 


205  2484 

7.  Which  is  greater,  9  times  4  or  7  times  5  ? 

8.  How  many  legs  has  one  chair  ?    How  many 
legs,  then,  will  nine  chairs  have  ? 

9.  How  many  fingers  has  one  boy?     How 
many  fingers,  then,  will  nine  boys  have  ? 

10.  Ada's  father  gives  her  and  her  8  brothers 
6  cents  each.     How  much  does  he  give  them  all  ? 

11.  I  have  five  hens,  and  each  hen  has  nine 
chickens.     Hens  and  chickens,  how  many  have  1? 

12.  How  much  will  nine  turkeys  weigh,  if 
their  weight  is  eight  pounds  apiece  ? 

13.  There  are  nine  chains,  each  six  feet  long. 
What  is  the  length  of  the  whole  nine  ? 

14.  How  many  gallons  in  9  ten-gallon  casks  ? 

Eepeat  the  even  tens :  10,  20,  30,  40,  50,  &c. 


10  times  1  is  10. 

10  times  2  is  20. 

10  times  3  is  30. 

10  times  4  is  40. 

10  times  5  is  50. 


10  times 

6  is 

60. 

10  times 

7  is 

70. 

10  times 

8  is 

80 

10  times 

9  is 

90 

10  times  10  is  100. 


! 

70  MULTIPLICATION. 


LESSON    LXVII. 

1        2  What  is  an  easy  way  of  multiply- 

10      10      ing  a  number  by  10  ? 
10      20  Ans.  Placing  a  naught  after  it? 

1.  Write  down  these  numbers ;  multiply  them 
by  10  in  the  way  just  shown  : — 

Eight  hundred  and  forty-seven. 
Six  hundred  and  seventy-nine. 
Two  hundred  and  thirteen. 
Seven  hundred  and  five. 
Thirty-three.    Nineteen.     Fifty-one. 

2.  Ten  cents  make  a  dime  ;  ten  dimes  make  a 
dollar.  How  many  cents,  then,  in  a  dollar? 
How  many  cents  are  seven  dimes  worth  ? 

3.  If  you  can  buy  two  apples  for  a  cent,  how 
many  can  you  get  for  ten  cents  ? 

4.  Ann  is  five  years  old.  If  she  lives  to  be 
ten  times  as  old,  what  will  be  her  age? 

5.  How  many  quarts  will  ten  jars  contain,  if 
each  holds  three  quarts  ? 

6.  At  3  cents  each,  what  will  10  oranges  cost  ? 

7.  There  are  nine  inches  in  a  quarter  of  a 
yard ;  how  many  inches  in  ten  quarters  ? 

8.  If  for  ten  days  you  get  four  good  marks 
each  day,  how  many  do  you  get  in  all  ? 

Review  all  the  Tables,  from  page  60,  till  you 
can  say  them  perfectly. 


MULTIPLYING   BY   ONE   FIGUKE.  71 


LESSON    LXVIII. 

Multiply     734 
By  6 

\ 

Look  at  the  above  example.  Always  begin  to 
multiply  at  the  right. 

6  times  4  is  24 — 4  units  and  2  tens.  Write 
the  4  units  in  the  units'  place,  and  add  the  2  tens 
to  the  next  product. 

6  times  3  tens  are  18  tens,  and  2  tens  are  20 
tens — or  2  hundreds.  Write  0  in  the  tens'  place, 
and  add  2  hundreds  to  the  next  product. 

6  times  T  hundreds  are  42  hundreds,  and  2 
hundreds  are  44  hundreds.     Answer,  4404. 

When,  in  multiplying  by  a  single  figure,  we 
get  a  product  expressed  by  two  figures,  what  must 
we  do  with  them  ? 

Ans.  We  must  place  the  right-hand  figure  of 
the  product  under  the  figure  rrmltiplied^  and  add 
the  left-hand  figure  to  the  next  product. 

If  36  is  your  product,  what  do  you  do  with 
each  figure?     If  63?    If  72? 

Examples  follow ;  multiply  as  shown  above,     i 

Multiply    863  638  742  914       ^ 

By  4  5  7  9 

3452    3190    5194    "8226 


72 

MTSCELLANBOFS   EXAMPLES. 

IiESSON   LXIZ. 

What] 

is  Numeration  ?    What  is  Notation  ? 

What 

is  Addition 

?     What  is  Subtraction? 

What  is  Multiplication  ? 

EXAMPLES 

FOB  THS 

,  SLATE. 

<i) 

(2) 

(3) 

(4) 

(«) 

Add    987 

846 

869 

1752 

789 

236 

155 

456 

990 

2789 

795 

383 

978 

2671 

789 

121 

353 

519 

2532 

2789 

143 

625 

780 

898 

1789 

422 

831 

659 

1098 

339 

(6) 

(7) 

(8) 

(9) 

(10) 

From      96 

410 

863 

1002 

3507 

Tako       38 

307 

264 

109 

1238 

(11) 

(12) 

(13) 

(14) 

(15) 

Multiply 

81 

72 

39 

160 

263 

By 

3 

6 

2 

8 

4 

(16) 

(17) 

(18) 

(19) 

(20) 

Multiply 

72 

90 

85 

698 

549 

By 

5 

10 

7 

10 

9 

:^i 


MISCELLANEOUS   EXAMPLES.  73 


LESSON    IiXX 

What  is  the  result,  or  answer,  called  in  Ad- 
dition ?  What,  in  Subtraction  ?  What,  in  Mul- 
tiplication ? 

1.  What  is  the  sum  of  four  hundred  and  sixty- 
one,  five  hundred  and  eighty-four,  and  seven 
huudred  and  two  ? 

2.  What  is  the  product  of  eight  hundred  and 
seventy-two,  and  nine  ? 

3.  If  forty-six  is  taken  from  eight  thousand 
and  twenty-nine,  what  is  the  remainder? 

4.  How  many  pages  in  nine  books,  if  each 
book  has  two  hundred  and  eighty-eight  pages? 

5.  One  book  has  four  hundred  and  fifty  pages ; 
another  has  two  hundred  and  sixty-four.  How 
many  pages  have  both  books  together?  How 
many  more  pages  has  one  than  the  other  ? 

6.  If  a  man  reads  forty-nine  books  every  year, 
how  many  will  he  read  in  ten  years  ? 

7.  A  gardener  set  out  a  hundred  and  nineteen 
trees  every  week  for  five  weeks.  If  95  out  of 
the  whole  number  died,  how  many  lived  ? 

8.  Maud's  uncle  left  his  whole  property  to 
her  and  her  five  brothers,  giving  them  each  one 
thousand  and  fifty  dollars.  What  was  he  worth 
in  all? 

9.  Multiply  a  thousand  and  twelve  by  eight. 


74  MULTIPLYING   BY   TWO   FIGFEES. 


LESSON    LXZI. 

Multiplj  609  by  18.    Let  us  see  how 
509      we  are  to  multiply  by  two  figures. 

Write  18  under   509,  units  under 


4072        units,  tens  under  tens. 
^^^  18  consists  of  8  units  and  1  ten.  "We 

9162  therefore  multiply  first  by  8  units,  and 
then  by  1  ten,  and  add  the  two  prod- 
ucts. 

Multiplying  by  8  units,  as  already  shown,  we 
get  4072  for  the  product. 

Now  multiply  by  1  ten.  Once  9  is  9.  Write 
it  in  the  tens^  jolace^  because  you  are  multiplying 
by  1  ten^  not  1  unit.  Once  0  is  0.  Once  5  is  5. 
The  product  is  509  tens, 

ISTow  add  the  two  products.    Answer,  9162. 

When  multiplying  hy  a  figure  in  the  tens^ 
place^  write  the  first  figure  of  the  product  in  the 
tens"^  place. 

In  finding  the  product  of  two  numbers^  multi- 
ply hy  the  one  that  has  the  fewer  figures. 

Examples  follow ;  multiply  as  shown  above. 

Multiply        87  260  159 

By  24  38  56 

348  2080  954 

174  780  795 


Product     2088  9880  8904 


MULTIPLICATION.  75 


XiESSON   LXXII. 

When  0  occurs  in  the  number  you  multiply 
by 5  how  do  you  proceed  ? 

Ans.  Bring  down  the  0,  and  go  on  multiply- 
ing by  the  next  figure,  all  in  the  same  line. 

Multiply  97  by  30.  97 

Bring  down  the  0.     Then  multiply      ^ 

by  3,  writing  the  result  in  the  same  line.         2910 

3   times  7  is   21.     Write   1   in   the 
tens'  place,  and  add  2  to  the  next  product.     3 
times  9  is  27,  and  2  are  29.     Answer,  2910. 

What  is  an  easy  way  of  multiplying  a  number 
by  100? 

Ans.  Placing  two  naughts  after  it. 

How  much  does  57  multiplied  by  100  make  ? 

Multiply  19  by  100.  Multiply  100  by  19. 
Which  is  the  greater  ? 

What  is  the  product  of  65  and  100  ? 

EXAMPLES  FOB  THE   SLATE. 

(1)  (2)  (3)  (4)  (5) 

Multiply  27        81         90  98         190 

By         16        37        24  95  26 


(6)  (7)  (8)  (9)  (10) 

Multiply  34        57        68  90  43 

By         20         89         50         100         100 


(7) 

(8) 

(9) 

57 

68 

90 

89 

50 

100 

76 


DIVISION. 


LESSON    LXXIII. 


Two   oxen   make    a    yoke. 

How  many  yoke  will  4  make  ? 

Model. — As  many  yoke  as   2  is  con- 
tained tiraes  in  4, — or  2.     Answer,  2  yoke. 


How     many 
yoke  will  6  oxen 
^    make  ? 


Finding  how  many  times  2 


"What  is  finding  how  many  times  one  number 
is  contained  in  another  called  ? 

Ans,  Dividing. 
is  contained  in  6,  is  dividing  6  by  2 

What  is  meant  by  dividing  9  by  3  ? 

Ans.  Finding  how  many  times  3  is  contained 
in  9. 

When  we  divide,  what  is  the  result  called  ? 

Ans,  The  Quotient.     Two  is  contained   in   6 
three  times  ;  3  is  the  quotient. 

When  we  divide  by  1,  what  is  the  quotient. 

Ans,    The    same   as    the    number    divided. 
Thus :— 


l.in  1,  once. 

1  in     6, 

6  times. 

1  in  2,  twice. 

1  in     7, 

7  times. 

1  in  3,  3  times. 

1  in     8, 

8  times. 

1  in  4,  4  times. 

1  in     9, 

9  times. 

1  in  5,  5  times. 

1  in  10, 

10  times. 

DIVISIOIT. 


77 


LEISSON   IiZXIV. 

What  is  Division  ? 

Ans.  Division  is  the  process  of  finding  how 
many  times  one  number  is  contained  in  another. 

What  is  the  result  called  in  Division  ? 

How  many  times  is  one  apple  contained  in 
one  apple  ?  In  five  apples  ?  In  ten  ?  In  four- 
teen? In  a  hundred  apples?  In  a  thousand 
apples  ? 

How  many  times  will  1  go  into  3  ?     Into  27  ? 

Divide  415  by  1,  and  what  is  the  quotient  ? 

How  many  times  is  2  contained  in  4  ?     In  6  ? 
Two  make  a  pair.     How  many  pair  will  8 
rabbits  make  ?     Count  and  see. 


How  many  pair  will  ten  horses  make  ? 


WS^^S^^ 

^M 

^^g' 

\ 

6  times. 

2  in     2,  once. 

2  in  12, 

2  in     4,  twice. 

2  in  14, 

7  times. 

2  in     6,  3  times. 

2  in  16, 

8  times. 

2  in     8,  4  times. 

2  in  18, 

9  times. 

2  in  10,  5  times. 

2  in  20, 

10  times. 

78  DIVISION. 


LESSON    LXXV. 

1.  Two  make  a  brace.     If  a  sportsman  shoots 
20  pheasants,  how  many  brace  has  he  ? 

Model. — He  has  as  many  brace  as  2  is  contained  times 
in  20,— or  10.    Answer,  10  brace. 

Follow  this  model  in  the  mental  examples  in  Division, 

2.  Two  make  a  couple.    If  a  group  of  16 
boys  pair  off,  how  many  couples  will  they  make? 

3.  How  many  pair  will  twelve  gloves  make  ? 

4.  If  16  cents  are  divided  equally  between 
two  poor  men,  how  many  cents  will  each  get  ? 

5.  Amy  and  her  sister  divided  14  chestnuts 
equally  between  them.     How  many  had  Amy  ? 

When  a  thing  is  divided 
into  two  equal  parts,  each 
part  is  called  a  Half. 

What  is  the  half  of  14  ?     Of  18  ? 

How  many  times  is  1  contained  in  1  ?   2  in  2  ? 
When  we  divide  any  number  by  itself,  what  is 
the  quotient  ?  Ans.  1. 

How  many  times  is  3  contained  in  3  ? 


3  in     3,  once. 
3  in     6,  twice.  , 
3  in     9,  3  times. 
3  in  12,  4  times. 
3  in  15,  5  times. 


3  in  18,  6  times. 
3  in  21,  7  times. 
3  in  24,  8  times. 
3  in  27,  9  times. 
3  in  30,  10  times. 


DIVISION.  79 


LESSON    liXXVI. 


How  mucli  is  3  times  2  ?  . 

How  many  times  is  3  contained  in  6  ?   2  in  6  ? 

1.  It  takes  three  lines  to  form  a 
triangle.      How  many  triangles  will 


twenty-one  lines  form  ? 

2.  How  many  cents  will  15  apples  cost,  at  the 
rate  of  3  for  a  cent  ? 

3.  If  we  walk  three  miles  an  hour,  how  many 
hours  will  it  take  us  to  walk  twelve  miles? 

4.  If  3  pounds  of  butter  last  a  family  a  week, 
how  many  weeks  will  thirty  pounds  last  them  ? 

5.  Twenty-four  is  how  many  times  three  ? 

6.  How  much  is  half  of  18?  How  many 
times  3  is  9  ? 

One  half  of  18  is  how  many  times  3  ? 

7.  One  half  of  6  is  how  many  times  3  ? 

8.  If  it  takes  3  feet  to  make  a  yard,  how 
many  yards  are  there  in  27  feet  of  ribbon? 

9.  Thomas  divided  eighteen  almonds  equally 
among  his  three  sisters ;  how  many  did  he  give 
each  ?     How  often  will  6  go  into  18  ? 


4  in     4,  once. 
4  in     8,  twice. 
4  in  12,  3  times. 
4  in  16,  4  times. 
4  in  20,  '5  times. 


4  in  24,  6  times. 

4  in  28,  7  times. 

4  in  32,  8  times. 

4  in  36,  9  times. 

4  in  40,  10  times. 


80 


DIVISION. 


4)1208 


LSSSON    LXXVII. 

Any  number  is  contained  in  0,  0  times. 

1  in  0,  0  times.     2  in  0,  0  times.     3  in  0, 
0  times,  &c. 

Divide  1208  by  4,  on  your  slate. 

Write  4,  the  number  you  divide 
by,  at  the  left  of  the  other  number 
with  a  line  between. 

In  dividing,  always  commence  at  the  left. 

As  you  find  the  quotient,  write  it  under  the 
number  divided. 

4  is  not  contained  in  1.    See,  then,  how  many 
times  it  is  contained  in  12,  the  first  two  figures. 

4  in  12,  3  times.     Write  3  under  the  2. 

Write  it  down.  4)  1208 

Write  down  2* 


4  in  0,  0  times. 


(1) 

4)204 


4  in  8,  twice.     Write  down  %       Arts,       302 
Some  examples  for  your  slate  follow : — 

(2)  (3)  (4)  (6) 

4)808        2)682        2)  1020        3)9630 


(6) 

1)768 


(7) 

2)168 


(8) 

3)186 


(9) 

3)2109 


(10) 

3) 3009 


5  in    5,  once. 
5  in  10,  twice. 
5  in  15,  3  times. 
5  in  20,  4  times. 
5  in  25,  5  times. 


5  in  30,     6  times. 

5  in  35,     7  times. 

5  in  40,     8  times. 

5  in  45,     9  times. 

5  in  50,  10  times. 


DIVISION.  81 


LESSON    LXXVIII. 

1.  If  four  wheels  are  needed  for  one  ear,  how 
many  cars  will  twenty-eight  wheels  supply  ? 

Model. — If  4  wheels  are  needed  for  one  car,  28  wheels 
will  supply  as  many  cars  as  4  is  contained  times  in  28, —or 
7  cars.    Answer,  7  cars. 

2.  A  farmer  distributes  40  pigs  equally  in 
four  pens.     How  many  does  he  put  in  each  ? 

3.  A  man  who  earns  4  dollars  a  week,  is  paid 
24  dollars.     For  how  many  weeks  is  he  paid  ? 

4.  If  I  place  four  boys  on  a  bench,  how  many 
benches  shall  I  need  for  thirty-six  boys  ? 

5.  If  5  oranges  are  worth  as  much  as  15 
apples,  how  many  apples  is  one  orange  worth  ? 

6.  If  five  rocking-horses  cost  forty -five  dollars, 
how  much  do  they  cost  apiece  ? 

7.  How  many  dresses  will  12  yards  of  ribbon 
trim,  if  it  takes  4  yards  to  trim  one  dress  ? 

8.  Four  pecks  make  a  bushel ;  how  many 
bushels  will  16  pecks  make? 

9.  If  one  pew  holds  five  persons,  how  many 
pews  will  it  take  to  hold  thirty  persons  ? 


0  in     6,  once. 

6  in  12,  twice. 

6  in  18,  3  times. 

6  in  24,  4  times. 

6  in  30,  5  times. 


6  in  36,  6  times. 
6  in  42,  7  times. 
6  in  48,  8  times. 
6  in  54,  9  times. 
6  in  60,  10  times. 


82  DIVISION, 


LESSON    LXXIX. 
EXAMPLES    EOR     THE     SLATE. 

1.  Divide  twelve  hundred  by  4.  Divide  it 
by  6.    Divide  it  by  3. 

2.  Divide  two  thousand  five  hundred  and  five 
by  five. 

3.  Divide  four  thousand  eight  hundred  and 
sixty  by  six.     Divide  it  by  two. 

,    4.  How  many  times  is  five  contained  in  thirty- 
five  hundred  and  fifty-five  ? 

5.  How  many  times  is  six  contained  in  three 
thousand  six  hundred  and  six  ? 

6.  If  two  thousand  dollars  be  divided  equally 
among  five  persons,  how  much  will  each  get  ? 

7.  If  four  hundred  and  twenty  books  are 
distributed  equally  on  six  shelves,  how  many 
will  there  be  on  each  shelf? 

8.  If  four  hundred  soldiers  are  divided  into 
5  companies,  how  many  will  there  be  in  each  ? 

9.  If  four  partners  together  make  two  thou- 
sand dollars  in  one  year,  how  much  is  that 
apiece  ? 


7  in    7,  once. 

7  in  14,  twice. 

7  in  21,  3  times. 

7  in  28,  4  times. 

7  in  35,  5  times. 


7  in  42,  6  times. 

7  in  49,  7  times. 

7  in  56,  8  times. 

7  in  63,  9  times. 

7  in  70,  10  times. 


DIVISION.  83 


IiSSSON    LXXX. 

1.  Euth  is  sent  to  divide  18  cakes  equally 
among  her  6  sisters.  How  many  must  she  give 
each? 

2.  How  many  classes  of  six  scholars  each  can 
be  formed  out  of  fifty-four  scholars  ? 

3.  Allowing  six  candles  to  the  pound,  how 
many  pounds  are  there  in  thirty-six  candles  ? 

4.  How  many  books  can  be  made  out  of  60 
sheets  of  paper,  if  it  takes  6  sheets  to  make  one 
book? 

5.  Paul  has  4  cents,  and  Eose  has  20.  They 
put  their  money  together,  and  divide  it  equally 
among  6  poor  girls.  How  much  does  each  girl 
get? 

6.  If  one  horse  can  draw  as  much  as  7  men, 
how  many  horses  will  draw  as  much  as  56  men  ? 

7.  How  many  weeks  of  7  days  each  are  there 
in  49  days  ? 

8.  I  am  63  years  old,  and  am  just  7  times  the 
age  of  my  son.    How  old  is  my  son  ? 

9.  Seven  times  two  is  how  many  times  seven  ? 


8  in     8,  once. 

8  in  48,     6  times. 

8  in  16,  twice. 

8  in  56,     7  times. 

8  in  24,  3  times. 

8  in  64,     8  times. 

8  in  32,  4  times. 

8  in  72,     9  times. 

8  in  40,  5  times. 

8  in  80,  10  times. 

84 


DIVISION. 


LBSSON    LXXXI. 


These  eight  boys  are  having  a  fine  sail. 

If  they  are  charged  40  cents  for  the  boat,  how 
much  will  each  have  to  pay  ? 

If  they  catch  24  fish  and  divide  them  equally, 
how  many  will  each  get  ? 

If  they  have  16  apples,  how  many  will  there 
be  for  each  boy  ? 

How  many  times  eight  is  the  half  of  16  ? 


9  in     9,  once. 

9  in  18,  twice. 

9  in  27,  3  times. 

9  in  36,  4  times. 

9  in  45,  5  times. 


9  in  54,  6  times. 

9  in  63,  7  times. 

9  in  72,  8  times. 

9  in  81,  9  times. 

9  in  90,  10  times. 


DIVISION. 


85 


LESSON    LXXXII. 

EXAMPLES    FOR    THE     SLATE. 

1.  If  one  stage-coach  will  hold  9  passengers, 
how  many  such  coaches  will  it  take  to  hold 
ninety-nine  passengers  ? 

2.  How  many  nine-gallon  jars  will  it  take  to 
hold  two  hundred  and  seventy  gallons? 

3.  If  a  family  use  nine  pounds  of  coffee  in  a 
month,  how  long  will  one  hundred  and  eighty- 
nine  pounds  last  them  ? 

4.  How  many  sets  of  9  volumes  each  can  be 
made  up  out  of  nine  thousand  and  ninety  volumes  ? 

5.  If  three  thousand  two  hundred  and  eight 
dollars  be  divided  among  eight  heirs,  how  many 
dollars  will  each  receive  ? 

6.  If  there  are  eight  panes  of  glass  in  one 
window,  how  many  windows  will  four  hundred 
and  eighty-eight  panes  supply  ? 

7.  Divide  eight  thousand  one  hundred  by  9. 
Write  down  the  even  tens  up  to  100 : — 10, 

20,  30,  &c. 


10  in  10,  once. 
10  in  20,  twice. 
10  in  30,  3  times. 
10  in  40,  4  times. 
10  in  50,  5  times. 


10  in 

60, 

6  times 

10  in 

w, 

7  times 

10  in 

80, 

8  times. 

10  in 

90, 

9  times. 

10  in  100,  10  times. 


QUESTIONS   IN"  DIVISION. 


LESSON   LXXXIII. 

What  is  Numeration  ?     What  is  Notation  ? 

What  is  Addition  ?     What  is  Subtraction  ? 

What  is  Multiplication  ?     What  is  Division  ? 

What  is  the  result,  or  answer,  called  in  Ad- 
dition? What  in  Subtraction?  What  in  Mul- 
tiplication ?     What  in  Division  ? 

1.  Ten  cents  make  a  dime.  How  many  dimes 
in  fifty  cents  ? 

2.  Ten  -  dimes  make  a  dollar.  How  many 
dollars  in  eighty  dimes  ? 

3.  Ten  dollars  make  an  eagle.  How  many 
eagles  in  thirty  dollars  ? 

4.  How  many  companies  of  ten  men  each  can 
be  formed  out  of  ninety  men  ? 

5.  Charles  has  7  dollars,  and  Eobert  3.  They 
put  their  money  together,  and  buy  ten  turkeys. 
What  do  the  turkeys  cost  apiece? 

6.  A  man  riding  10  miles  an  hour,  travels  20 
miles.     How  many  hours  is  he  on  the  way  ? 

7.  If  ten  omnibus  tickets  cost  60  cents,  what 
does  one  ticket  cost  ? 

EXAMPLES   FOR   THE    SLATE. 
(1)  (2)  (3)  (4) 

8)7208    9)7290    9)  3699    10)  7000 


DIVISION.  87 


LESSON    LXXXIV. 

How  often  is  6  contained  in  7  ? 

Ans,  It  is  contained  once  /  for  6  in  6,  once. 

It  is  not  contained  twice  ;  for  twice  6  is  12. 

Is  6  contained  in  7  once  exactly  ? 

Ans,  No ;  6  is  contained  once  exactly  in  6. 
As  7  is  one  more  than  6,  we  say  that  6  goes  into 
7  ^/i(?^,  and  one  over. 

How  often  is  6  contained  in  20  ? 
"  ^n5.  6  in  18,  3  times ;  18  from  20  leaves  2. 
Hence  6  goes  into  20  j^Ar^^  times^  and  two  over. 

How  many  times  is  3  contained  in  26  ?  4  in 
38?     7  in  50?     2  in  21?     8  in  55  ?     5inM? 

What  is  that  which  is  left  over  called  ? 
Ans,  The  Remainder. 

If  we  come  to  a  figure  too  small  to  contain 
the  one  we  are  dividing  by,  what  do  we  do  ? 

Ans,  If  it  is  not  the  first  figure,  we  write  0  in 
the  quotient. 

Divide  3604  by  6. 

6)  3604 

Quotient       600,  and  4  remainder. 

Divide,  as  above,  on  your  slate  :  (1.)  635  by  9. 
(2.)  563  by  8.  (3.)  4089  by  4.  (4.)  621  by  2. 
(5.)  6308  by  3.     (6.)  499  by  7.     (7.)  4009  by  5. 


88  DIVISION. 


LBSSON    LXXXV. 

^  ^  Divide  3901  by  4.    Commence 

4)  3901  at  the  left.    4  is  not  contained  in 

975, 1  rem.  3.  Scc,  then,  how  often  it  will  go 
into  39,  the  first  two  figures. 

4  in  39,  9  times  and  3  over.  "Write  9  under 
the  9,  and  prefix  the  remainder  3,  in  your  mind, 
to  the  next  figure — making  30. 

4  in  30,  7  times  and  2  over.  Write  7  under 
the  0,  and  prefix  2  to  the  next  figure — mak- 
ing 21. 

4  in  21,  5  times  and  1  over.  Place  5  under 
the  1,  and  the  remainder  1  to  the  right.  Answer  : 
quotient  975,  and  1  remainder. 

When,  before  all  the  figures  have  been  di- 
vided, we  have  a  remainder,  what  must  be  done 
with  it? 

Ans,  We  must  prefix  it,  in  the  mind,  to  the 
next  figure  to  be  divided. 

Examples  follow ;  divide  as  shown  above. 

(1)  (2)  (3) 

2)1349  3)^904  4)1762 

Quo.     674,  1  rem.  Quo.     968  Quo.     440,  2  rem. 

(4)  (5)  (6)  (7) 

5)  2564         6)  6702  8)  9679  9)4235 


DIVIDING   BY   TEN.  89 


LESSON    LXXXVI. 

Divide  4017  by  10.  ^0^  4017 

10  in  40,  4  times.    Write  4  ^--— 

under  the  0.  401,  7  rem. 

10  in  1,  0  times  and  1  over.  "Write  0  under 
the  1,  and  prefix  1  to  the  next  figure.  10  in 
17,  once  and  7  over.  Write  1  under  the  7,  and  7 
as  remainder.    Answer,  401  and  7  remainder. 

Now  compare  this  answer  with  the  number 
to  be  divided — 4017.  It  is  the  same  as  if  we  had 
cut  off  the  right  hand  figure  for  the  remainder, 
and  taken  the  rest  for  the  quotient — 401 1 7. 

Give,  then,  an  easy  rule  for  dividing  by  10. 

Ans,  Cut  off  the  right-hand  figure  of  the 
number  to  be  divided  for  the  remainder,  and  tahe 
the  other  figures  for  the  quotient. 

Write  the  following  numbers.  Divide  them 
by  10  in  the  way  just  shown. 

1.  Five  thousand  two  hundred  and  nineteen. 

2.  Eighteen  hundred  and  sixty-three. 

3.  Nine  thousand  and  seventy-eight. 

4.  Eleven  hundred  and  eleven. 

5.  Four  thousand  one  hundred  and  forty. 

6.  Seven  thousand  two  hundred  and  six. 

7.  Nine  hundred  and  ninety-four. 

8.  Eight  thousand  and  one. 

9.  Nineteen  hundred  and  five. 


90  EXERCISE   Iiq-   ADDITION. 

LESSON    LXXXVII. 

What  sign  is  used  to  denote  Addition  ? 
Ans.  This  sign  +,  called  plus. 

What  does  4  +  5  mean  ? 
Ans,  It  is  read,  four  plus  Jive.    It  means  4 
added  to  5,  and  is  equal  to  9. 

When  numbers  are  to  be  added  or  subtracted, 
how  must  we  be  sure  to  write  them  down  ? 

Ans.  So  as  to  bring  units  under  units,  tens 
under  tens,  &c. 

Eead  the  following  examples.  Write  down 
the  numbers,  and  add  them  on  your  slate. 

1.  987+764-3665  +  544-2443.       Ans.  7225. 

2.  752  +  3953+414+6  +  1745.       Ans.  6870. 

3.  306  +  1032  +  89  +  567  +  765. 

4.  4+455  +  2260  +  1476  +  7+3488. 

5.  8  +  859  +  4954+483  +  1891  +  10  +  705. 

6.  10  +  758  +  655  +  950  +  62  +  969  +  863+737. 

7.  1659  +  2  +  2348  +  9  +  3299  + 1028  +  79  + 17. 

8.  1728  +  756  +  1699  +  789  +  1967+539  +  154. 
How  many  tens  must  we  add  together,  to  pro- 
duce 80  ?    Write  them  down,  and  add  them. 

How  many  one  hundreds  must  we  add,  in 
order  to  get  1000  ?  Write  them  down,  and  add 
them. 

What  is  the  sum  of  8  times  10,  and  10  times 
100? 


BXEECISB   IN  SUBTEACTION, 


91 


LESSON   I.ZXXVIII. 

What  sign  is  used  to  denote  Subtraction  ? 
Ans.  This  sign  — ,  called  minus. 

What  does  5  —  4  mean  ? 
Ans.  It  is  read^«  mmus  fo-ur.    It  means  4 
subtracted  from  5,  and  is  equal  to  1. 

When  minus  is  used,  which  is  the  number  to 
be  subtracted  ? 

Ans.  The  one  that  stands  after  the  minus. 


Eead  the  following. 

1.  1829  —  304. 

2.  4506  —  2702. 

3.  1234  —  899. 

4.  4108  —  1053. 

5.  2738  —  1374. 

6.  2345  —  1779. 

7.  2301  —  126. 

8.  6456  —  1679. 


Find  the  remainders. 

9.  3647  —  1753. 

10.  4567  —  2679. 

11.  7091  —  5132. 

12.  5678  —  1679. 

13.  9000  —  7889. 

14.  6789  —  3289. 

15.  7890  —  4719. 

16.  2006  —  1018. 


17.  Mr.  W.  has  2500  dollars  in  one  bank,  and 
5000  in  another.  He  buys  a  house  for  6000  dol- 
lars. If  he  draws  out  money  enough  to  pay  for 
it,  how  much  will  he  have  left  in  bank  ? 

18.  How  much  is  2500  +  5000  —  6000? 

19.  How  much  is  1422  +  2578  — 1510  ? 

20.  How  much  is  3761  +  5239  —  999? 


92 


EXERCISE   IN   MULTIPLICATION. 


liESSON   liXXZIX. 

What  sign  is  used  to  denote  Multiplication  ? 
Ans.  This  sign  x . 

What  does  4x5  mean  ? 
Ans.  It  vaennafour  multiplied  by  Jive,  and  is 
equal  to  20. 

Which  is  greater,  4  x  5  or  5  x  4  ? 

What  is  an  easy  way  of  multiplying  by  10  ? 

What  easy  way  of  multiplying  by  100  ? 

What  is  the  number  to  be  multiplied  called  ? 
Ans.  The  Multiplicand. 

What  is  the  number  you  multiply  by  called  ? 
Ans.  The  Multiplier. 

When  the  multiplier  contains  0,  how  were 
you  told  to  proceed  ? 


Read  the  following. 


Find  the  products. 


1. 
2. 
3. 
4. 


1605 

4198 

973 

861 

5.  1284 

6.  1066 

7.  851 

8.  2396 

9.  271 


6. 

2. 

9. 
10. 

7. 

5. 

8. 

4. 
36. 


10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 


62 
396 

57 
403 
189 
148 

82 
25 
65 


100. 

19. 

80. 

17. 

20. 

63. 

95. 
204. 

90. 


EXEECISE   IN  DIVISION. 


93 


LESSON    XC. 

What  sign  is  used  to  denote  Division  ? 

Ans.  This  sign  -v-. 

What  does  14  -r-  7  mean  ? 

Ans.  It  laesins  fourteen  divided  ly  seven^  and 
is  equal  to  2. 

When  the  sign  for  division  stands  between 
two  numbers,  which  is  to  be  divided  ? 

Ans.  The  one  before  it  is  to  be  divided  by 
the  one  after  it. 

What  is  the  number  to  be  divided  called  ? 

Ans.  The  Dividend. 

What  is  the  number  you  divide  by  called  ? 

Ans.  The  Divisor. 

What  easy  rule  was  given  for  dividing  by  10  ? 

Kead  the  following.  Find  the  quotient  and 
remainder. 


1.  8064  - 

r  4. 

2.  9193  - 

-  3. 

3,  2709  - 

-  9. 

4.  4004  - 

-  5. 

5.  7777  - 

-  2. 

6.  1941  - 

-  10. 

7.  1468  - 

-  1. 

8.  2496  - 

-  7. 

9.  5684  -. 

-  6. 

10.  4713 

11.  6565 

12.  3709 

13.  2723 

14.  3379 

15.  6055 

16.  7327 

17.  5403 

18.  2670 


5. 
9. 
8. 
4. 
6. 
3. 
8. 
7. 
10. 


94:  MISCELLANEOUS    EXAMPLES. 

LESSON    XCI. 

PEOMISCUOUS   MENTAL   EXAMPLES. 

1.  If  a  man  earns  15  dollars  a  week,  and 
spends  9,  how  much  will  he  save  in  4  weeks  ? 
How  much  in  6  weeks  ? 

First  find  how  mucli  he  will  save  in  1  week,  then  in  4. 

2.  Ellen  puts  aside  3  cents  every  day  for  the 
poor,  and  James  puts  aside  5  cents.  How  much 
will  they  both  have  for  the  poor  in  a  week  ? 

3.  We  collect  10  dollars  for  the  poor  one  day, 
and  6  the  next.  If  we  divide  the  whole  among 
4  poor  families,  how  much  will  each  get  ? 

4.  Mary  reads  2  pages  every  morning,  and  7 
every  afternoon  ;  how  many  pages  does  she  read 
in  a  week  ? 

5.  If  10  peaches  fill  a  quart  measure,  how 
many  quart  measures  will  80  peaches  fill  ? 

6.  A  farmer  has  3  white  hens  and  4  black 
ones.  If  each  hen  hatches  4  chickens,  how  many 
chickens  will  the  farmer  have  ? 


HALVES,   THIRDS,   FOURTHS.  95 

LESSON    XOII. 

When  a  thing  is  divided  into  2 
equal  parts,  what  is  each  part  called  ? 
Ans.  A  Half. 

How  many  halves  in  a  whole  pear  ?     Count 
and  see. 

When  a  thing  is  divided  into  3 
equal  parts,  what  is  each  part  called  ? 
Ans,  A  Third. 
How  many  thirds  in  a  whole  pear  ? 

When  a  thing  is  divided  into  4 
equal  parts,  what  is  each  part  called  ?  ^ 
Ans.  A  Fourth,  or  Quarter. 

How  many  fourths,  or  quarters,  in  a  whole 
pear  ?     Count  and  see. 

What  is  this  line  divided  into  ? 

-- 

What  is  this  line  divided  into  ? 
What  is  this  line  divided  into  ? 


Which  is  greater,  a  half,  a  third,  or  a  fourth  \ 
Look  at  the  lines  divided  above,  and  see. 


I 

96  FK  ACTIONS. 


LESSON    XCIII. 


If  a  whole  is  divided  into  5  equal  parts,  each 
part  is  called  one  Fifth. 

lilt' 

If  a  whole  is  divided  into  6  equal  parts,  each 
part  is  called  one  Sixth. 

■■         »  * 

If  a  whole  is  divided  into  7  equal  parts,  each 
part  is  called  one  Seventh. 

If  a  whole  is  divided  into  8  equal  parts,  each 
part  is  called  one  Eighth. 

II        I        I        I        I        1        f 

If  a  whole  is  divided  into  9  equal  parts,  each 
part  is  called  one  Ninth. 

If  a  whole  is  divided  into  10  equal  parts,  each 
part  is  called  one  Tenth. 

What  are  such  equal  parts  of  a  whole  called  ? 
Ans.  Fractions. 

Learn  how  to  write  these  fractions : — 


One  half 
One  third 
One  fourth 


1 


One  fifth  1 
One  sixth  } 
One  seventh  4 


One  eighth  | 
One  ninth  ^ 
One  tenth     j\ 


FRACTIONS. 


97 


LESSON    XOIV. 


Learn  this  table  : — 

2  halves,  one  whole. 

3  thirds,    one  whole. 

4  fourths,  one  whole. 

5  fifths,     one  whole. 


6  sixths,      one  whole. 

7  sevenths,  one  whole. 

8  eighths,    one  whole. 

9  ninths,     one  whole. 


10  tenths,  one  whole. 

Since  2  halves  make  a  whole,  to  find  one  halt 
cut  the  whole  into  2  equal  parts. 

To  find  half  of  a  number,  divide  it  by  2. 


To  find  1,  divide  by  3. 
To  find  ^,  divide  by  4. 
To  find  j,  divide  by  5. 
To  find  ^,  divide  by  6. 


To  find  I,  divide  by  7. 
To  find  I,  divide  by  8. 
To  find  i,  divide  by  9. 
To  find  j^„  divide  by  10. 


EXAMPLES   FOE   THE   SLATE. 

1.  What  is  1  of  6184?    Of  298?     Of  336? 

2.  What  is  i  of  369  ?    Of  1482  ?     Of  1578  ? 

3.  Find  one  tenth  of  8970.     Of  2310.    Of  80. 

4.  What  is  i  of  2548?     Ot  332?     Of  380? 

5.  Find  one  sixth  of  1812.     Of  924.     Of  342. 

6.  Find  i  of  2808.      Of  6534.     Of  4851. 

7.  Find  i  of  4060.     Of  3750.     Of  4005. 

8.  Take  i  of  1752.     Of  7008.     Of  3224. 

9.  Take  1  of  5810.     Of  3325.     Of  693. 


98 


FEDERAL   MONEY. 


LESSON   XCV. 


Now  we  must  learn  about  money,  weights,  &c. 

What  is  the  money  of  the  United  States 
called  ?  Ans.  Federal  Money. 


Cent. 


TABLE   OF   FEDERAL   MONEY. 

10  mills  make  1  cent. 
10  cents,  1  dime. 

10  dimes,  1  dollar. 

10  dollars,        1  eagle. 


Dime. 


Eagle.  Eagle. 

Besides  these,  we  have  other  coins : — 

The  three  cent  piece,  worth  3  cents. 
The  half- dime,  worth    5  cents. 

The  quarter-dollar,     worth  25  cents. 
^The  half-dollar,  worth  50  cents. 

The  quarter-eagle,  worth  2^  dollars. 
The  half-eagle,  worth  5  dollars. 
The  double  eagle,  worth  20    dollars. 


FEDERAL   MONEY.  99 

IiESSON   XGVI. 

What  mark  is  used  to  denote  dollars  ? 

Ans,  This  mark  $,  placed  t^ore  the  number. 

Twenty  dollars  is  written  $20. 

Twenty  dollars,  six  cents,  is  written  $20.06 

Twenty  dollars,  thirteen  cents,  $20.13 

Twenty  dollars,  twelve  cents,  1  mill,  $20,121 

Twenty  dollars,  one  mill,  $20,001 

The  first  two  figures  after  the  period  denote 
cents.     The  third  figure  denotes  mills. 

$60,019  is  read  sixty  dollars,  one  cent,  9  mills. 
$4,502,  four  dollars,  fifty  cents,  two  mills. 

Eead  and  add  the  following.     In  setting  them 
down,  let  the  periods  all  range  in  line. 

1.  $103.24 + $47.91  +  $3008.008  -f  $546,356. 

2.  $6000.009  4-  $652.88  +  $1267 + $987,765. 

3.  $800.81 4-  $6793.054 + $21,421  +  $1896. 

4.  $9,428  +  $4200.919  +  $87.75  +  $365.66. 

5.  From  eighty-seven  dollars,  forty     $87,405 
cents,  five  mills,  take  ten  dollars,  ninety-       l^-^l 
one  cents.  Ans.  $ 

6.  From  nine  hundred  dollars,  take  thirty-two 
dollars,  seventy-three  cents,  five  mills. 

7.  From    fifty    dollars,   seventy    cents,    take 
nineteen  dollars,  one  cent,  six  mills. 


100  EXERCISES   IN   FEDERAL  MONEY. 

LESSON   XOVII. 

1.  A  lady  buys  7  pounds  of  meat  at  10  cents  L 
a  pound ;  how  much  must  she  give  for  it  ? 

If  she  hands  the  butcher  a  dollar  bill,  how 
much  change  must  he  give  her  ? 

2.  Robert  buys  a  slate  for  10  cents,  and  a 
book  for  40  cents.  He  gives  the  store-keeper  half 
a  dollar.     How  much  change  must  he  receive  ? 

3.  John  buys  half  of  a  six  cent  pie,  and  hands 
the  baker  a  dime.   How  much  change  will  he  get  ? 

4.  How  many  cents  make  a  dime  ?  How  many 
cents  are  5  dimes  worth  ?     9  dimes  ?     10  dimes  ? 

1  dollar  ? 

5.  How  many  dollars  make  an  eagle  ?  How 
many  eagles  in  40  dollars  ?     In  80  dollars  ? 

6.  How  many  dollars  is  a  half-eagle  worth  ? 

2  half-eagles  ?     5  half-eagles  ?     10  half-eagles  ? 

7.  How  many  half-dimes  are  equal  to  10 
cents  ?    To  30  cents  ?    To  60  cents  ?    To  a  dollar? 

8.  I  leave  home  with  an  eagle  in  my  pocket. 
I  spend  $4  in  market,  and  on  my  way  home  give 
10  beggars  a  dime  each.     How  much  have  I  left  ? 

9.  If  a  man  deposits  an  eagle  in  the  savings 
bank  every  week,  how  many  dollars  will  he  have 
there  in  ten  weeks  ? 

10.  How  many  dimes  in  one  eagle  ? 

11.  If  a  boy  gives  a  store-keeper  a  dollar,  and 
gets  25  cents  change,  how  much  has  he  spent  ? 


STERLING   MONEY.  101 

LESSON    XOVIII. 

What  is  the  money  of  Great  Britain  called  ? 
Ana-  English  or  Sterling  Money. 

Sovereign. 
X(^^^^S\         TABLE   OF   STERLING   MONEY. 

/^H^^T?''^     4  farthings  make  1  penny. 
||  ^^^^1  ||  12  pence,  1  shilling. 

\r^^^/y    2^  shillings,  1  pound. 

^^113^^      21  shillings,  1  guinea. 

What  mark  is  used  to  denote  pounds  ? 

Ans.  This  mark  £,  placed  before  the  number. 

What  coin  represents  1  pound  ? 
Ans.  The  sovereign,  a  gold  coin. 

How  many  shillings  is  1  sovereign  worth  ? 
Ans.  Twenty  shillings. 

Which  is  worth  more,  a  sovereign  or  a  guinea  ? 

1.  How  many  farthings  in  1  penny  ?     In  8 
pence  ?    In  10  pence  ? 

2.  What  part  of  a  penny  is  a  farthing  ? 

3.  How  many  farthings  in  a  half-penny  ? 

4.  If  I  pay  9  shillings  for  a  map,  and  £1  for 
a  book,  which  costs  the  more  ?   How  much  more  ? 

5.  If  a  boy  who  has  £2  spends  half  of  it,  how 
many  shillings  has  he  left  ? 

6.  Five  beggars  received  8  farthings  each. 
How  many  pence  did  that  make  for  all  five  ? 


102  TROY   WEIGHT. APOTHECAEIEs', 


LESSON   XOIX. 

TROY   WEIGHT. 

"What  is  Troy  weight  used  in  weighing  ? 
Ans.  Gold,  silver,  and  precious  stones. 

TABLE. 

24  grains  make      1  pennyweight. 
20  pennyweights,  1  ounce. 
12  ounces,  1  pound. 


APOTHECARIES'  WEIGHT. 

By  whom  is  Apothecaries'  weight  used  ? 
Ans.  By  apothecaries,  in  mixing  medicines. 

TABLE. . 

20  grains  make  1  scruple. 
3  scruples,         1  dram. 
8  drams,  1  ounce. 

K     12  ounces,  1  pound. 

1.  A  person  who  has  a  pound  of  gold  dust,  sells 
4  ounces  of  it.     How  many  ounces  has  he  left  ? 

2.  How  many  spoons  weighing  10  penny- 
weights each  will  it  take  to  make  an  ounce  ? 

3.  How  many  powders  of  5  grains  each  can  a 
druggist  make  out  of  1  scruple  of  calomel  ? 

4.  How  many  drams       in  2  ounces  ?    In  8 
ounces  ?    In  11  ounces  ? 


AVOIRDUPOIS   WEIGHT. 


103 


LESSON    C. 

AVOIRDUPOIS  WEIGHT. 

What  is  Avoirdupois  Weight  used  for  ? 
Ans.  For  weighing  the  metals  except  gold 
and  silver,  groceries,  and  all  coarse  goods. 


TABLE. 


16  drams  make. 


16  ounces, 
25  pounds, 
4  quarters, 
20  hundred-weight,    1  ton. 


1  ounce. 

1  pound. 

1  quarter. 

1  hundred-weight, 


1.  How  many  cornucopias  holding  4  ounces 
each  can  be  filled  with  a  pound  of  candy  ? 

2.  How  many  pounds  in  a  quarter? 


hundred-weight  ? 


In  20  hundred-weight  ? 


In  a 
In  a 


ton? 

3.  How  many  pounds  in  2  tons  of  coal  ? 

4.  Emma  weighs  just  half  as  much  as  Charles, 
and  he  weighs  80  pounds.  What  is  Emma's 
weight  ? 

5.  If  a  grocer  sells  two  boys  half  a  pound  of 
cheese  each,  how  many  ounces  is  that  in  all  ? 

6.  If  5  pounds  are  used  out  of  a  quarter  of 
flour,  how  many  pounds  are  left  ? 

Y.  If  a  hundred-weight  of  pork  is  divided 
among  10  men,  how  many  pounds  will  each  have  ? 


104:  LONG   MEASURE. 


LESSON    CI. 

LONG  MEASURE. 


For  what  is  Long  Measure  used  ? 

Ans.  For  measuring  length  and  distance. 


One  inch. 

Make  a  line  one  inch  long  on  your  slate. 

TABLE. 

12    inches  make  1  foot. 

3    feet,  1  yard. 

5|-  yards,  1  rod  or  pole. 

40    rods,  1  furlong. 

8    furlongs,  1  mile. 

1.  How  many  inches  long  is  a  yard-stick  ? 

2.  A  boy  who  has  to  walk  a  mile  to  town, 
has  gone  half  the  way.  How  many  furlongs  has 
he  yet  to  go  ? 

3.  A  tall  man  is  6  feet  high.  How  many 
yards  is  that  ? 

4.  Allowing  a  yard  to  each  step,  how  many 
feet  will  a  man  go  in  10  steps  ? 

5.  How  many  rods  in  a  furlong?  In  8  fur- 
longs ?     In  a  mile  ? 

6.  About  how  many  inches  wide  is  this  page  ? 

7.  How  many  inches  in  a  quarter  of  a  yard  ? 


LIQUID   MEASITRE. 


105 


LESSON    CII. 


LIQUID    MEASURE. 


For  what  is  Liquid  Measure  used  ? 
Ans.  For  measuring  liquids;    such  as  milk, 
oilj  vinegar,  molasses,  liquors,  &c. 


T  ABL  E. 

p 

4    gills  make  1  pint. 

m 

2    pints, 

1  quart. 

JSafl 

4    quarts. 

1  gallon. 

JHj 

^Ji  ■  y 

31i  gallons. 

1  barrel. 

ffigi 

1^^^ 

2  barrels. 

1  hogshead. 

^^m 

2  hogsheads. 

1  pipe. 

^Hr 

2  pipes. 

1  tun. 

~B 

4HliTI 

1.  A  tumbler  holds  about  half  a  pint ;  how 
many  tumblerfuls  in  a  quart  ? 

2.  How  many  pints  will  fill  a  quart  measure  ? 

3.  If  a  milkman  mixes  2  pints  of  water  with 
4  quarts  of  milk,  how  much  will  he  have  in  all  ? 

4.  Suppose  half  a  gallon  leaks  out  of  a  barrel 
of  oil ;  how  many  gallons  remain  in  it  ? 

5.  How  many  quart  pitchers  can  be  filled 
from  a  two-gallon  pail  ? 

6.  How  many  barrels  will  a  pipe  of  wine  fill  ? 

7.  If  I  have  8  quarts  of  cider,  and  give  half 
of  it  away,  how  many  gallons  have  I  left  ? 


106  DRY   MEASURE. 


LESSON   CIII. 

DRY  MEASURE. 

For  what  is  Dry  Measure  used  ? 
Ans.  For  measuring  fruit,  vegetables,  coal, 
salt,  grain,  &c. 

TABLE. 

2  pints  make  1  quart. 
8  quarts,         1  peck. 
4  pecks,  1  bushel. 

36  bushels,       1  chaldron. 
The  dry  quart  measure  is  of  wood  ;  the  liquid 
quart  measure  is  of  tin. 

A  small  measure  contains  2  quarts. 


1.  A  man  bought  a  bushel  of  apples ;  if  one 
peck  was  rotten,  how  many  pecks  were  good  ? 

2.  How  many  quarts  in  a  half  peck  ? 

3.  If  a  horse  eats  8  quarts  of  oats  a  day,  how 
long  will  it  take  him  to  eat  a  bushel  ? 

4.  If  a  pint  of  chestnuts  costs  6  cents,  what 
will  a  quart  cost  ? 

5.  If  5  girls  go  a  berrying,  and  each  girl  picks 
a  quart,  how  many  pints  will  they  have  in  all  ? 

6.  Which  are  cheaper,  potatoes  at  a  dollar  a 
bushel,  or  30  cents  a  peck  ? 

7.  What  is  a  peck  of  corn  worth,  at  80  cents 
a  bushel  ? 


TIME  MEASURE.                                  107 

LESSON 

OIV. 

TIME  MEASURE. 

60  seconds  make  1  minute. 
60  minutes,           1  hour. 
24  hours,               1  day. 
7  days,                 1  week. 

365  days,      •          1  year. 

366  days,                 1  leap  year. 
100  years,                1  century. 

How  many  calendar  m 
Ans.  Twelve. 

onths  in  a  year  ? 

Name  the  calendar  months  of  the  year  in  order, 
and  the  number  of  days  in  each. 

1st  month,  January, 

31. 

7th  mo. 

July, 

31. 

2d    month,  February, 

28. 

8th  mo. 

August, 

31. 

3d   month,  March, 

31. 

9th  mo. 

September, 

30. 

4th  month,  April, 

30. 

10th  mo. 

,  October, 

31. 

5th  month,  May, 

31. 

11th  mo. 

November, 

30. 

6  th  month,  June, 

30. 

12th  mo. 

December, 

31. 

These  days  added  together  make  365  days  in 
the  year.  In  Leap  Year,  February  is  one  day 
longer,  and  the  whole  number  of  days  is  366. 

There  are  four  seasons  in  the  year : — 
Spring,  consisting  of  March,  April,  May ; 
Summer,  June,  July,  August ; 
Autumn  or  Fall,  September,  October,  November ; 
Winter,  December,  January,  February. 


108  MISCELLANEOUS   TABLE. 

LESSON    OV. 

MISCELLANEOUS   TABLE. 

(  12  tilings  make   1  dozen. 

(  12  dozen,  1  gross. 

20  things,  1  score. 

(  24  sheets,  1  quire  of  paper. 

(  20  quires,  1  ream. 

56  pounds,  1  firkin  of  butter. 

100  pounds,  1  quintal  of  fish. 

196  pounds,  1  barrel  of  flour. 

200  pounds,  1  barrel  of  pork. 


1.  Which  weighs  more,  a  barrel  of  flour  or  a 
barrel  of  pork,  and  how  much  ? 

2.  If  a  man  lives  to  be  ''  three  score  years  and 
ten,"  how  old  is  he  ? 

3.  A  box  of  pens  holds  a  gross ;  how  many 
dozen  in  a  box  ?     How  many  pens  in  a  box  ? 

4.  How  many  sheets  in  one  fourth  of  a  quire 
of  paper  ? 

5.  If  five  pounds  of  butter  are  taken  out  of  a 
full  firkin,  how  many  pounds  will  remain  ? 

6.  How  many  pounds  in  5  quintals  of  codfish  ? 

7.  Which  month  is  the  shortest  in  the  year  ? 

8.  John  was  to  stay  in  the  city  a  week.  He 
has  been  there  5  days ;  how  much  longer  is  he 
to  stay  ? 


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YA  04350 


54 1 1 92 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


.y 


APPLETONS' 

ARITHMETICAL  SERIES. 

By  G.  P.  QUACK  KNBCS,  i^L.  D. 
Upon  the  basis  of  the  Works  oi  HF/  mh  «.  fEHRlNS,  LL.D. 


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